Engineering: Civil - Major #3011

Certificate of Achievement Program Map

The program map below represents an efficient and effective course taking sequence for this program. Individual circumstances might require some changes to this path. It is always recommended that you meet with your pathway counselor to develop a personalized educational plan.


This certificate of achievement is designed as basic coursework necessary for pursuing a career in the field of civil engineering.

Upon completion of the program, students will:
  1. 1. An ability to apply knowledge, techniques, skills and modern tools of mathematics, science, engineering, and technology to solve broadly-defined engineering problems appropriate to the discipline.
  2. 2. An ability to design systems, components, or processes meeting specified needs for broadly-defined engineering problems appropriate to the discipline.
  3. 3. An ability to apply written, oral, and graphical communication in broadly-defined technical and non-technical environments; and an ability to identify and use appropriate technical literature.
  4. 4. An ability to conduct standard tests, measurements, and experiments and to analyze and interpret the results to improve processes.
  5. 5. An ability to function effectively as a member or leader on a technical team.
Effective Term: 2026 Fall Semester

Term 1

10-12 units

ENGR 10
Introduction to Engineering

2 units
Effective Term: 2025 Spring Semester
This course explores the branches of engineering, the functions of an engineer, and the industries in which engineers work. Explains the engineering education pathways and explores effective strategies for students to reach their full academic potential. Presents an introduction to the methods and tools of engineering problem solving and design including experimentation, data analysis, computer and communication skills, and the interface of the engineer with society and engineering ethics. (A, CSU, UC)
Course Details:
  1. Advisory: ENGL C1000

MATH C2210
Calculus I: Early Transcendentals

5 units
Effective Term: 2026 Fall Semester
Part 1: A first course in differential and integral calculus of a single variable. Topics include limits and continuity of functions, techniques and applications of differentiation, an introduction to integration, and the Fundamental Theorem of Calculus. This course is primarily intended for Science, Technology, Engineering, and Mathematics (STEM) majors.
Part 2: (A, CSU, UC, Cal-GETC)
Course Details:
  1. Prerequisite:

Math placement may vary depending on multiple measures (high school math, previous math course taken at another institution, etc.)

Major Core

3-5 units

Select one of the following: 

CHEM 1A
General Chemistry I

5 units
Effective Term: 2025 Fall Semester
Development of atomic theory; atoms, isotopes, molecules, and ions; compounds; classification of matter; formulas and equations; stoichiometry; introduction to aqueous reactions: precipitation, acids and bases, and gas forming and redox reactions; gas laws; kinetic molecular theory of gases; thermochemistry; modern atomic theory; VSEPR theory; valence bond (hybridization) and molecular orbital theories; intermolecular forces; properties of liquids; solids and crystal structures; solution behavior; colligative properties; associated laboratory experiments; and volumetric (titrimetric) and gravimetric analysis methods. (A, CSU, UC, Cal-GETC)
Course Details:
    (
  1. Prerequisite: MATH 3A
  2. AND
  3. Prerequisite: CHEM 3A
  4. )

ENGR 1A
Elementary Plane Surveying 1

4 units
Effective Term: 2025 Fall Semester
Principles and practice of plane surveying: office computations and design; operation of surveying field equipment; and production of engineering plans/maps. Topics include distances, angles, and directions; differential leveling; traversing; property/boundary surveys; topographic surveys/mapping; volume/earthwork; horizontal and vertical curves; land description techniques; and GPS. Extensive field work using tapes, levels, total stations, and GPS/GNSS equipment. (A, CSU, UC)
Course Details:
  1. Prerequisite: MATH 4A
  2. Advisory: ENGL C1000

ENGR 2
Graphics

4 units
Effective Term: 2023 Spring Semester
Principles of engineering drawings in visually communicating engineering designs and an introduction to computer-aided design (CAD). Topics include the development of visualization and sketching skills, orthographic projections, mechanical dimensioning and tolerancing practices, 2D and 3D CAD skills and the engineering design process. The use of CAD software is an integral part of the course. (A, CSU, UC)
Course Details:
  1. Prerequisite: MATH 4A

ENGR 4
Engineering Materials

3 units
Effective Term: 2023 Spring Semester
Properties of engineering materials and their relation to atomic structure. The effect of microstructure on the mechanical, electrical, magnetic and thermal properties. Phase equilibria and strengthening processes for metals, ceramics, and polymers. (A, CSU, UC)
Course Details:
    (
  1. Prerequisite: CHEM 1A
  2. AND
  3. Prerequisite: PHYS 4A
  4. )

ENGR 8
Statics

3 units
Effective Term: 2023 Spring Semester
Rigid bodies in static equilibrium when acted upon by forces and couples in two- and three-dimensional space. Included are the equilibrium of rigid bodies, trusses, frames, and machines, as well as the calculations of the centers of mass, centroids, friction, and moments of inertia. Additional topics which may be covered include distributed forces in cables, beams, and fluid statics; mass moments of inertia; and virtual work. (A, CSU, UC)
Course Details:
  1. Prerequisite: PHYS 4A
  2. Corequisite: MATH 6

GEOL 1
Physical Geology

4 units
Effective Term: 2025 Fall Semester
This course consists of an introduction to the principles and unifying concepts of earth science including geologic time, formation and internal structure of the Earth, plate tectonics, rock and mineral identification, weathering processes, landforms, earthquakes, volcanic activity, flooding and groundwater resources. Laboratory exercises will include rock and mineral identification, and interpretation of topographic and geologic maps. Optional field trips to classic geologic locations. (A, CSU, UC, Cal-GETC)
Course Details:

    MATH 7 or MATH 17

    4-5 units
    MATH 7
    Introduction to Differential Equations
    4 units
    Effective Term: 2024 Fall Semester
    This course is an introduction to ordinary differential equations including applications from a variety of disciplines. The course introduces the theoretical aspects of differential equations, including establishing when solution(s) exist, and techniques for obtaining solutions, including, series solutions, Laplace transforms and linear systems. This course is not intended for students who have taken Math 17. (A, CSU, UC)
    Course Details:
    1. Anti Requisite: MATH 17
    2. (
    3. Prerequisite: MATH 6
    4. OR
    5. Prerequisite:
    6. )
    or
    MATH 17
    Differential Equations and Linear Algebra
    5 units
    Effective Term: 2025 Fall Semester
    This is an introductory course in ordinary differential equations and linear algebra. Topics for this course include first-order ordinary differential equations, including separable, linear, homogeneous of degree zero, Bernoulli and exact with applications and numerical methods. Students will also study solutions to higher order differential equations using undetermined coefficients, variation of parameters, power series, with applications; solutions to linear and non-linear systems of differential equations, including numerical solutions; matrix algebra, solutions of linear systems of equations, and determinants; vector spaces, linear independence, basis and dimension, subspace and inner product space, including the Gram-Schmidt procedure; as well as linear transformations, kernel and range, eigenvalues, eigenvectors, diagonalization and symmetric matrices. (A, CSU, UC, Cal-GETC)
    Course Details:
    1. Prerequisite: MATH 6

    PHYS 4C
    Physics for Scientists and Engineers

    4 units
    Effective Term: 2026 Fall Semester
    Oscillations, waves, thermodynamics, optics, relativity, quantum mechanics, and nuclear physics. Designed primarily for physics, engineering, and related majors. (A, CSU, UC, Cal-GETC)
    Course Details:
    1. Prerequisite: PHYS 4A
    2. Corequisite: MATH C2220
    3. Advisory: MATH 6

    Term 2

    12-14 units

    MATH C2220
    Calculus II: Early Transcendentals

    5 units
    Effective Term: 2026 Fall Semester
    Part 1: A second course in differential and integral calculus of a single variable. Topics include applications of integration, techniques of integration, infinite sequences and series, and the calculus of parametric and polar equations. This course is primarily intended for Science, Technology, Engineering, and Mathematics (STEM) majors.
    Part 2: (A, CSU, UC, Cal-GETC)
    Course Details:
    1. :

    PHYS 4A
    Physics for Scientists and Engineers

    4 units
    Effective Term: 2026 Fall Semester
    Classical mechanics: kinematics, Newton's Laws, energy, momentum, gravitation, and fluids. Designed primarily for physics, engineering, and related majors. (A, CSU, UC, Cal-GETC)
    Course Details:
    1. Corequisite: MATH C2220

    Major Core

    3-5 units

    Select one of the following: 

    CHEM 1A
    General Chemistry I

    5 units
    Effective Term: 2025 Fall Semester
    Development of atomic theory; atoms, isotopes, molecules, and ions; compounds; classification of matter; formulas and equations; stoichiometry; introduction to aqueous reactions: precipitation, acids and bases, and gas forming and redox reactions; gas laws; kinetic molecular theory of gases; thermochemistry; modern atomic theory; VSEPR theory; valence bond (hybridization) and molecular orbital theories; intermolecular forces; properties of liquids; solids and crystal structures; solution behavior; colligative properties; associated laboratory experiments; and volumetric (titrimetric) and gravimetric analysis methods. (A, CSU, UC, Cal-GETC)
    Course Details:
      (
    1. Prerequisite: MATH 3A
    2. AND
    3. Prerequisite: CHEM 3A
    4. )

    ENGR 1A
    Elementary Plane Surveying 1

    4 units
    Effective Term: 2025 Fall Semester
    Principles and practice of plane surveying: office computations and design; operation of surveying field equipment; and production of engineering plans/maps. Topics include distances, angles, and directions; differential leveling; traversing; property/boundary surveys; topographic surveys/mapping; volume/earthwork; horizontal and vertical curves; land description techniques; and GPS. Extensive field work using tapes, levels, total stations, and GPS/GNSS equipment. (A, CSU, UC)
    Course Details:
    1. Prerequisite: MATH 4A
    2. Advisory: ENGL C1000

    ENGR 2
    Graphics

    4 units
    Effective Term: 2023 Spring Semester
    Principles of engineering drawings in visually communicating engineering designs and an introduction to computer-aided design (CAD). Topics include the development of visualization and sketching skills, orthographic projections, mechanical dimensioning and tolerancing practices, 2D and 3D CAD skills and the engineering design process. The use of CAD software is an integral part of the course. (A, CSU, UC)
    Course Details:
    1. Prerequisite: MATH 4A

    ENGR 4
    Engineering Materials

    3 units
    Effective Term: 2023 Spring Semester
    Properties of engineering materials and their relation to atomic structure. The effect of microstructure on the mechanical, electrical, magnetic and thermal properties. Phase equilibria and strengthening processes for metals, ceramics, and polymers. (A, CSU, UC)
    Course Details:
      (
    1. Prerequisite: CHEM 1A
    2. AND
    3. Prerequisite: PHYS 4A
    4. )

    ENGR 8
    Statics

    3 units
    Effective Term: 2023 Spring Semester
    Rigid bodies in static equilibrium when acted upon by forces and couples in two- and three-dimensional space. Included are the equilibrium of rigid bodies, trusses, frames, and machines, as well as the calculations of the centers of mass, centroids, friction, and moments of inertia. Additional topics which may be covered include distributed forces in cables, beams, and fluid statics; mass moments of inertia; and virtual work. (A, CSU, UC)
    Course Details:
    1. Prerequisite: PHYS 4A
    2. Corequisite: MATH 6

    GEOL 1
    Physical Geology

    4 units
    Effective Term: 2025 Fall Semester
    This course consists of an introduction to the principles and unifying concepts of earth science including geologic time, formation and internal structure of the Earth, plate tectonics, rock and mineral identification, weathering processes, landforms, earthquakes, volcanic activity, flooding and groundwater resources. Laboratory exercises will include rock and mineral identification, and interpretation of topographic and geologic maps. Optional field trips to classic geologic locations. (A, CSU, UC, Cal-GETC)
    Course Details:

      MATH 7 or MATH 17

      4-5 units
      MATH 7
      Introduction to Differential Equations
      4 units
      Effective Term: 2024 Fall Semester
      This course is an introduction to ordinary differential equations including applications from a variety of disciplines. The course introduces the theoretical aspects of differential equations, including establishing when solution(s) exist, and techniques for obtaining solutions, including, series solutions, Laplace transforms and linear systems. This course is not intended for students who have taken Math 17. (A, CSU, UC)
      Course Details:
      1. Anti Requisite: MATH 17
      2. (
      3. Prerequisite: MATH 6
      4. OR
      5. Prerequisite:
      6. )
      or
      MATH 17
      Differential Equations and Linear Algebra
      5 units
      Effective Term: 2025 Fall Semester
      This is an introductory course in ordinary differential equations and linear algebra. Topics for this course include first-order ordinary differential equations, including separable, linear, homogeneous of degree zero, Bernoulli and exact with applications and numerical methods. Students will also study solutions to higher order differential equations using undetermined coefficients, variation of parameters, power series, with applications; solutions to linear and non-linear systems of differential equations, including numerical solutions; matrix algebra, solutions of linear systems of equations, and determinants; vector spaces, linear independence, basis and dimension, subspace and inner product space, including the Gram-Schmidt procedure; as well as linear transformations, kernel and range, eigenvalues, eigenvectors, diagonalization and symmetric matrices. (A, CSU, UC, Cal-GETC)
      Course Details:
      1. Prerequisite: MATH 6

      PHYS 4C
      Physics for Scientists and Engineers

      4 units
      Effective Term: 2026 Fall Semester
      Oscillations, waves, thermodynamics, optics, relativity, quantum mechanics, and nuclear physics. Designed primarily for physics, engineering, and related majors. (A, CSU, UC, Cal-GETC)
      Course Details:
      1. Prerequisite: PHYS 4A
      2. Corequisite: MATH C2220
      3. Advisory: MATH 6

      Term 3

      12-14 units

      MATH 6
      Mathematical Analysis III

      5 units
      Effective Term: 2026 Fall Semester
      This course includes solid analytical geometry; partial differentiation; integral calculus of multivariable functions; two and three dimensional vectors; vector valued functions; topics in vector calculus including Green’s, Divergence, and Stokes’ Theorems. (A, CSU, UC, Cal-GETC)
      Course Details:
        (
      1. Prerequisite: MATH C2220
      2. OR
      3. Prerequisite:
      4. )

      PHYS 4B
      Physics for Scientists and Engineers

      4 units
      Effective Term: 2026 Fall Semester
      Electricity and magnetism: electrostatics, electric potential, DC circuits, magnetic fields, induction, and AC circuits. Designed primarily for physics, engineering, and related majors. (A, CSU, UC, Cal-GETC)
      Course Details:
      1. Prerequisite: PHYS 4A
      2. Corequisite: MATH C2220
      3. Advisory: MATH 6

      Major Core

      3-5 units

      Select one of the following:

      CHEM 1A
      General Chemistry I

      5 units
      Effective Term: 2025 Fall Semester
      Development of atomic theory; atoms, isotopes, molecules, and ions; compounds; classification of matter; formulas and equations; stoichiometry; introduction to aqueous reactions: precipitation, acids and bases, and gas forming and redox reactions; gas laws; kinetic molecular theory of gases; thermochemistry; modern atomic theory; VSEPR theory; valence bond (hybridization) and molecular orbital theories; intermolecular forces; properties of liquids; solids and crystal structures; solution behavior; colligative properties; associated laboratory experiments; and volumetric (titrimetric) and gravimetric analysis methods. (A, CSU, UC, Cal-GETC)
      Course Details:
        (
      1. Prerequisite: MATH 3A
      2. AND
      3. Prerequisite: CHEM 3A
      4. )

      ENGR 1A
      Elementary Plane Surveying 1

      4 units
      Effective Term: 2025 Fall Semester
      Principles and practice of plane surveying: office computations and design; operation of surveying field equipment; and production of engineering plans/maps. Topics include distances, angles, and directions; differential leveling; traversing; property/boundary surveys; topographic surveys/mapping; volume/earthwork; horizontal and vertical curves; land description techniques; and GPS. Extensive field work using tapes, levels, total stations, and GPS/GNSS equipment. (A, CSU, UC)
      Course Details:
      1. Prerequisite: MATH 4A
      2. Advisory: ENGL C1000

      ENGR 2
      Graphics

      4 units
      Effective Term: 2023 Spring Semester
      Principles of engineering drawings in visually communicating engineering designs and an introduction to computer-aided design (CAD). Topics include the development of visualization and sketching skills, orthographic projections, mechanical dimensioning and tolerancing practices, 2D and 3D CAD skills and the engineering design process. The use of CAD software is an integral part of the course. (A, CSU, UC)
      Course Details:
      1. Prerequisite: MATH 4A

      ENGR 4
      Engineering Materials

      3 units
      Effective Term: 2023 Spring Semester
      Properties of engineering materials and their relation to atomic structure. The effect of microstructure on the mechanical, electrical, magnetic and thermal properties. Phase equilibria and strengthening processes for metals, ceramics, and polymers. (A, CSU, UC)
      Course Details:
        (
      1. Prerequisite: CHEM 1A
      2. AND
      3. Prerequisite: PHYS 4A
      4. )

      ENGR 8
      Statics

      3 units
      Effective Term: 2023 Spring Semester
      Rigid bodies in static equilibrium when acted upon by forces and couples in two- and three-dimensional space. Included are the equilibrium of rigid bodies, trusses, frames, and machines, as well as the calculations of the centers of mass, centroids, friction, and moments of inertia. Additional topics which may be covered include distributed forces in cables, beams, and fluid statics; mass moments of inertia; and virtual work. (A, CSU, UC)
      Course Details:
      1. Prerequisite: PHYS 4A
      2. Corequisite: MATH 6

      GEOL 1
      Physical Geology

      4 units
      Effective Term: 2025 Fall Semester
      This course consists of an introduction to the principles and unifying concepts of earth science including geologic time, formation and internal structure of the Earth, plate tectonics, rock and mineral identification, weathering processes, landforms, earthquakes, volcanic activity, flooding and groundwater resources. Laboratory exercises will include rock and mineral identification, and interpretation of topographic and geologic maps. Optional field trips to classic geologic locations. (A, CSU, UC, Cal-GETC)
      Course Details:

        MATH 7 or MATH 17

        4-5 units
        MATH 7
        Introduction to Differential Equations
        4 units
        Effective Term: 2024 Fall Semester
        This course is an introduction to ordinary differential equations including applications from a variety of disciplines. The course introduces the theoretical aspects of differential equations, including establishing when solution(s) exist, and techniques for obtaining solutions, including, series solutions, Laplace transforms and linear systems. This course is not intended for students who have taken Math 17. (A, CSU, UC)
        Course Details:
        1. Anti Requisite: MATH 17
        2. (
        3. Prerequisite: MATH 6
        4. OR
        5. Prerequisite:
        6. )
        or
        MATH 17
        Differential Equations and Linear Algebra
        5 units
        Effective Term: 2025 Fall Semester
        This is an introductory course in ordinary differential equations and linear algebra. Topics for this course include first-order ordinary differential equations, including separable, linear, homogeneous of degree zero, Bernoulli and exact with applications and numerical methods. Students will also study solutions to higher order differential equations using undetermined coefficients, variation of parameters, power series, with applications; solutions to linear and non-linear systems of differential equations, including numerical solutions; matrix algebra, solutions of linear systems of equations, and determinants; vector spaces, linear independence, basis and dimension, subspace and inner product space, including the Gram-Schmidt procedure; as well as linear transformations, kernel and range, eigenvalues, eigenvectors, diagonalization and symmetric matrices. (A, CSU, UC, Cal-GETC)
        Course Details:
        1. Prerequisite: MATH 6

        PHYS 4C
        Physics for Scientists and Engineers

        4 units
        Effective Term: 2026 Fall Semester
        Oscillations, waves, thermodynamics, optics, relativity, quantum mechanics, and nuclear physics. Designed primarily for physics, engineering, and related majors. (A, CSU, UC, Cal-GETC)
        Course Details:
        1. Prerequisite: PHYS 4A
        2. Corequisite: MATH C2220
        3. Advisory: MATH 6

        Term 4

        34-35 units

        ENGR 5
        Programming and Problem Solving in MATLAB

        3 units
        Effective Term: 2026 Fall Semester
        Utilizes the MATLAB environment to provide students with a working knowledge of computer-based problem solving methods relevant to science and engineering. Introduces the fundamentals of procedural and object-oriented programming, numerical analysis, and data structures. Examples and assignments in the course are drawn from practical applications in engineering, physics, and mathematics. (A, CSU, UC)
        Course Details:
        1. Prerequisite: MATH C2210

        Major Core

        31-32 units

        Select one of the following: 

        CHEM 1A
        General Chemistry I

        5 units
        Effective Term: 2025 Fall Semester
        Development of atomic theory; atoms, isotopes, molecules, and ions; compounds; classification of matter; formulas and equations; stoichiometry; introduction to aqueous reactions: precipitation, acids and bases, and gas forming and redox reactions; gas laws; kinetic molecular theory of gases; thermochemistry; modern atomic theory; VSEPR theory; valence bond (hybridization) and molecular orbital theories; intermolecular forces; properties of liquids; solids and crystal structures; solution behavior; colligative properties; associated laboratory experiments; and volumetric (titrimetric) and gravimetric analysis methods. (A, CSU, UC, Cal-GETC)
        Course Details:
          (
        1. Prerequisite: MATH 3A
        2. AND
        3. Prerequisite: CHEM 3A
        4. )

        ENGR 1A
        Elementary Plane Surveying 1

        4 units
        Effective Term: 2025 Fall Semester
        Principles and practice of plane surveying: office computations and design; operation of surveying field equipment; and production of engineering plans/maps. Topics include distances, angles, and directions; differential leveling; traversing; property/boundary surveys; topographic surveys/mapping; volume/earthwork; horizontal and vertical curves; land description techniques; and GPS. Extensive field work using tapes, levels, total stations, and GPS/GNSS equipment. (A, CSU, UC)
        Course Details:
        1. Prerequisite: MATH 4A
        2. Advisory: ENGL C1000

        ENGR 2
        Graphics

        4 units
        Effective Term: 2023 Spring Semester
        Principles of engineering drawings in visually communicating engineering designs and an introduction to computer-aided design (CAD). Topics include the development of visualization and sketching skills, orthographic projections, mechanical dimensioning and tolerancing practices, 2D and 3D CAD skills and the engineering design process. The use of CAD software is an integral part of the course. (A, CSU, UC)
        Course Details:
        1. Prerequisite: MATH 4A

        ENGR 4
        Engineering Materials

        3 units
        Effective Term: 2023 Spring Semester
        Properties of engineering materials and their relation to atomic structure. The effect of microstructure on the mechanical, electrical, magnetic and thermal properties. Phase equilibria and strengthening processes for metals, ceramics, and polymers. (A, CSU, UC)
        Course Details:
          (
        1. Prerequisite: CHEM 1A
        2. AND
        3. Prerequisite: PHYS 4A
        4. )

        ENGR 8
        Statics

        3 units
        Effective Term: 2023 Spring Semester
        Rigid bodies in static equilibrium when acted upon by forces and couples in two- and three-dimensional space. Included are the equilibrium of rigid bodies, trusses, frames, and machines, as well as the calculations of the centers of mass, centroids, friction, and moments of inertia. Additional topics which may be covered include distributed forces in cables, beams, and fluid statics; mass moments of inertia; and virtual work. (A, CSU, UC)
        Course Details:
        1. Prerequisite: PHYS 4A
        2. Corequisite: MATH 6

        GEOL 1
        Physical Geology

        4 units
        Effective Term: 2025 Fall Semester
        This course consists of an introduction to the principles and unifying concepts of earth science including geologic time, formation and internal structure of the Earth, plate tectonics, rock and mineral identification, weathering processes, landforms, earthquakes, volcanic activity, flooding and groundwater resources. Laboratory exercises will include rock and mineral identification, and interpretation of topographic and geologic maps. Optional field trips to classic geologic locations. (A, CSU, UC, Cal-GETC)
        Course Details:

          MATH 7 or MATH 17

          4-5 units
          MATH 7
          Introduction to Differential Equations
          4 units
          Effective Term: 2024 Fall Semester
          This course is an introduction to ordinary differential equations including applications from a variety of disciplines. The course introduces the theoretical aspects of differential equations, including establishing when solution(s) exist, and techniques for obtaining solutions, including, series solutions, Laplace transforms and linear systems. This course is not intended for students who have taken Math 17. (A, CSU, UC)
          Course Details:
          1. Anti Requisite: MATH 17
          2. (
          3. Prerequisite: MATH 6
          4. OR
          5. Prerequisite:
          6. )
          or
          MATH 17
          Differential Equations and Linear Algebra
          5 units
          Effective Term: 2025 Fall Semester
          This is an introductory course in ordinary differential equations and linear algebra. Topics for this course include first-order ordinary differential equations, including separable, linear, homogeneous of degree zero, Bernoulli and exact with applications and numerical methods. Students will also study solutions to higher order differential equations using undetermined coefficients, variation of parameters, power series, with applications; solutions to linear and non-linear systems of differential equations, including numerical solutions; matrix algebra, solutions of linear systems of equations, and determinants; vector spaces, linear independence, basis and dimension, subspace and inner product space, including the Gram-Schmidt procedure; as well as linear transformations, kernel and range, eigenvalues, eigenvectors, diagonalization and symmetric matrices. (A, CSU, UC, Cal-GETC)
          Course Details:
          1. Prerequisite: MATH 6

          PHYS 4C
          Physics for Scientists and Engineers

          4 units
          Effective Term: 2026 Fall Semester
          Oscillations, waves, thermodynamics, optics, relativity, quantum mechanics, and nuclear physics. Designed primarily for physics, engineering, and related majors. (A, CSU, UC, Cal-GETC)
          Course Details:
          1. Prerequisite: PHYS 4A
          2. Corequisite: MATH C2220
          3. Advisory: MATH 6
          Total: 68-75 units