Math 2415 - Calculus III - University of Houston

# Math 2415 - Calculus III

***This is a course guideline. Students should contact instructor for the updated information on current course syllabus, textbooks, and course content***

*This course was previously MATH 2433*

Section number: This information applies to all sections.

Delivery format: face-to-face lecture or online.

Prerequisites: MATH 2414

Course Description: Calculus of functions of several variables: calculus of vector-valued functions, partial differentiation, multiple integrals.

Textbook & Access Code: The textbook,online quizzes, and additional help materials will be made available by logging into CASA Campus Services (CCS) at https://ccs.casa.uh.edu/ . Students pay for access to CCS as part of their fee bill via CTAP. If one opts out of the CTAP, they can purchase an access code for this course at UH Bookstore. In this case, if the code is not entered by the deadline specified on CASA, students will lose access to CASA. No make ups will be given for assignments missed during the no-access period.

Upon successful completion of this course, students will:

• Perform calculus operations on vector‐valued functions, including derivatives, integrals, curvature, displacement, velocity, acceleration, and torsion.
• Perform calculus operations on functions of several variables, including partial derivatives, directional derivatives, and multiple integrals.
• Find extrema and tangent planes.
• Solve problems using the Fundamental Theorem of Line Integrals, Green's Theorem, the Divergence Theorem, and Stokes' Theorem.
• Apply the computational and conceptual principles of calculus to the solutions of real-world problems.

[Additional course curriculum details: Advanced topics in calculus, including vectors and vector-valued functions, partial differentiation, Lagrange multipliers, multiple integrals, and Jacobians; application of the line integral, including Green’s Theorem, the Divergence Theorem, and Stokes’ Theorem.]

Syllabus

Chapter 11. VECTORS

Section 11.1 Cartesian Space Coordinates
Section 11.2 Vectors
Section 11.3 The Dot Product
Section 11.4 The Cross Product
Section 11.5 Lines 11.6 Planes

Chapter 12. VECTOR CALCULUS

Section 12.1 Vector Functions
Section 12.2 Differentiation Formulas
Section 12.3 Curves
Section 12.4 Arc Length
Section 12.5 Curvilinear Motion; Curvature

Chapter 13. FUNCTIONS OF SEVERAL VARIABLES

Section 13.1 Basic Terms and Examples
Section 13.2 Graphs; Level Curves and Level Surfaces
Section 13.3 Limits and Continuity
Section 13.4 Partial Derivatives

Chapter 14. GRADIENTS; EXTREME VALUES; DIFFERENTIALS

Section 14.2 Gradients and Directional Derivatives
Section 14.3 The Mean-Value Theorem; Chain Rules
Section 14.4 The Gradient as a Normal; Tangent Lines and Tangent Planes
Section 14.5 Local Extreme Values
Section 14.6 Absolute Extreme Values
Section 14.7 LaGrange Multipliers; Maxima and Minima with Side Conditions
Section 14.8 Increments and Differentials
Section 14.9 Reconstructing a Function from Its Gradient

Chapter 15. DOUBLE AND TRIPLE INTEGRALS

Section 15.1 Double Integrals
Section 15.2 The Evaluation of Double Integrals by Repeated Integrals
Section 15.3 Evaluating Double Integrals Using Polar Coordinates
Section 15.4 Some Applications of Double Integration
Section 15.5 Triple Integrals
Section 15.6 Reduction to Repeated Integrals
Section 15.7 Cylindrical Coordinates
Section 15.8 Spherical Coordinates
Section 15.9 Jacobians; Changing Variables in Multiple Integration

Chapter 16. LINE INTEGRALS AND SURFACE INTEGRALS

Section 16.1 Line Integrals
Section 16.2 The Fundamental Theorem for Line Integrals
Section 16.3 Line Integrals With Respect to Arc Length
Section 16.4 Green’s Theorem
Section 16.5 Parameterized Surfaces; Surface Area
Section 16.6 Surface Integrals
Section 16.7 The Vector Differential Operator
Section 16.8 The Divergence Theorem
Section 16.9 Stokes’s Theorem