# 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.

More information on the Cougar Textbook Access Program (CTAP) & Canvas/CCS:

- CTAP: https://uh.edu/af-auxiliary-services/ctap/
- CTAP FAQs: https://uh.edu/af-auxiliary-services/ctap/ctap-faqs/

- Canvas: https://uh.edu/canvas/
- CCS login: https://ccs.casa.uh.edu/
- CCS Course Finder: https://crs.uh.edu/requests/student_course_finder.php

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 14.1 Differentiability and Gradient

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 15.2 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

**Grading:** Please consult your instructor's syllabus regarding any and all grading guidelines.

**Justin Dart Jr. Center Accommodations:**

**Academic Adjustments/Auxiliary Aids**: The University of Houston System complies with Section 504 of the Rehabilitation Act of 1973 and the Americans with Disabilities Act of 1990, pertaining to the provision of reasonable academic adjustments/auxiliary aids for students who have a disability. In accordance with Section 504 and ADA guidelines, University of Houston strives to provide reasonable academic adjustments/auxiliary aids to students who request and require them. If you believe that you have a disability requiring an academic adjustments/auxiliary aid, please visit Justin Dart Jr. Student Accessibility Center website at https://www.uh.edu/accessibility/ for more information.

**UH CAPS**

Counseling and Psychological Services (CAPS) can help students who are having difficulties managing stress, adjusting to college, or feeling sad and hopeless. You can reach (CAPS) by calling 713-743-5454 during and after business hours for routine appointments or if you or someone you know is in crisis. No appointment is necessary for the "Let's Talk" program, a drop-in consultation service at convenient locations and hours around campus.