Multivariable Calculus

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Department of Mathematics

Math2433 – Calculus III

Section number: This information applies to all sections.

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

Prerequisites: MATH 1432

Course Description: Calculus of functions of several variables: calculus of vector-valued functions, partial differentiation, multiple integrals. *Note: TCCNS Equivalent: MATH 2415

Textbook: Calculus, 9th Edition, by Salas, Hille, and Etgen, Wiley. Available in electronic form (PDF) through CASA for all enrolled students via an Access Code .

Homework Assignments

The information contained in this class outline is an abbreviated description of the course.  Additional important information is contained at your instructor’s personal webpage. You are responsible for knowing all of this information.

 

Syllabus

Chapter 12. VECTORS

Section 12.1 Cartesian Space Coordinates
Section 12.2 Displacements and Forces
Section 12.3 Vectors
Section 12.4 The Dot Product
Section 12.5 The Cross Product
Section 12.6 Lines
Section 12.7 Planes

Chapter 13. VECTOR CALCULUS

Section 13.1 Vector Functions
Section 13.2 Differentiation Formulas
Section 13.3 Curves
Section 13.4 Arc Length
Section 13.5 Curvilinear Motion; Curvature

EXAM I

Chapter 14. FUNCTIONS OF SEVERAL VARIABLES

Section 14.1 Elementary Examples
Section 14.2 A Brief Catalogue of Quadric Surfaces; Projections
Section 14.3 Graphs; Level Curves and Level surfaces
Section 14.4 Partial Derivatives
Section 14.5 Open and Closed Sets
Section 14.6 Limits and Continuity; Equality of Mixed Partials

Chapter 15. GRADIENTS; EXTREME VALUES; DIFFERENTIALS

Section 15.1 Differentiability and Gradient
Section 15.2 Gradients and Directional Derivatives
Section 15.3 The Mean-Value Theorem; Chain Rules
Section 15.4 The Gradient as a Normal; Tangent Lines and Tangent Planes
Section 15.5 Local Extreme Values
Section 15.6 Absolute Exreme Values
Section 15.7 Maxima and Minima with Side Conditions
Section 15.8 Differentials
Section 15.9 Reconstructing a Function from its Gradient

EXAM II

Chapter 16. DOUBLE AND TRIPLE INTEGRALS

Section 16.2 The Double Integral
Section 16.3 The Evaluation of Double Integrals by Repeated Integrals
Section 16.4 Double Integrals in Polar Coordinates
Section 16.6 Triple Integrals
Section 16.7 Reduction to Repeated Integrals
Section 16.8 Triple Integrals in Cylindrical Coordinates
Section 16.9 The Triple Integral as a Limit of Riemann Sums; Spherical Coordinates
Section 16.10 Jacobians; Changing Variables in Multiple Integration

Chapter 17. LINE INTEGRALS AND SURFACE INTEGRALS

Section 17.1 Line Integrals
Section 17.2 The Fundamental Theorem for Line Integrals
Section 17.3 Work-Energy Formula; Conservation of Mechanical Energy
Section 17.4 Line Integrals with Respect to Arc Length
Section 17.5 Green’s Theorem
Section 17.6 Parameterized Surfaces; Surface Area
Section 17.7 Surface Integrals
Section 17.8 The Vector Differential Operator
Section 17.9 The Divergence Theorem
Section 17.10 Stokes’s Theorem

EXAM III


Homework Problems

Chapter 12

    Section 12.1:   3, 4, 5, 7, 9, 12, 13, 15, 19, 20, 35, 37, 38, 41, 43, 45, 46
    Section 12.3:   1, 4, 7, 8, 10, 11, 15, 17, 19, 21, 23, 24, 25, 28, 30, 31, 33, 34, 41
    Section 12.4:   1, 3, 5, 8, 9, 11, 13, 14, 15, 17, 19, 21, 27, 29, 31, 32, 37, 38, 39, 44, 45, 46
    Section 12.5:   4, 5, 7, 8, 14, 15, 17, 18, 21, 23, 26, 28, 29, 34, 35, 38, 41, 45, 48
    Section 12.6:   1, 2, 3, 4, 7, 10, 11, 13, 17, 18, 19, 24, 25, 26, 27, 28, 34, 35
    Section 12.7:   1, 3, 6, 7, 10, 13, 17, 18, 21, 22, 23, 24, 28, 29, 35, 36, 37, 38, 46, 47, 51

Chapter 13

    Section 13.1:   3, 4, 7, 9, 10, 16, 19, 20, 21, 22, 27, 30, 31, 32, 34, 39, 40, 43, 46, 49
    Section 13.2:   3, 4, 7, 8, 14, 15, 16, 21, 22, 24, 25, 27, 32, 33
    Section 13.3:   1, 2, 4, 5, 9, 11, 12, 17, 18, 19, 21, 23, 24, 27, 29, 32, 35, 37, 38, 41
    Section 13.4:   1, 2, 3, 4, 8, 13, 15, 20, 23
    Section 13.5:   3, 4, 6, 10, 13, 17, 18, 21, 24, 27, 28, 31, 32, 35, 40, 41, 43, 46, 47

Chapter 14

    Section 14.1:   3, 4, 7, 9, 10, 15, 17, 20, 27, 29, 30, 35, 36, 37, 38
    Section 14.2:   13, 14, 15, 16, 19, 23, 45, 48, 49, 51
    Section 14.3:   2, 3, 7, 8, 13, 14, 19, 20, 21, 22, 27, 28, 31, 37, 42, 43, 45
    Section 14.4:   2, 5, 6, 8, 9, 11, 12, 15, 19, 20, 26, 31, 32, 43, 45, 46, 53, 55
    Section 14.5:   1, 2, 3, 4, 6, 7, 9
    Section 14.6:   2, 3, 4, 7, 13, 14, 15, 19, 20, 23, 26, 27, 28

Chapter 15

    Section 15.1:   1, 3, 5, 6, 9, 11, 12, 15, 17, 19, 20, 23, 26, 33, 34, 39, 40
    Section 15.2:   3, 4, 7, 9, 10, 15, 18, 19, 20, 21, 23, 26, 32, 37
    Section 15.3:   1, 2, 7, 10, 11, 13, 15, 17, 19, 20, 23, 29, 32, 33, 35
    Section 15.4:   1, 2, 5, 7, 11, 12, 14, 16, 20, 23, 25, 33, 34, 35
    Section 15.5:   2, 3, 5, 7, 9, 10, 13, 14, 20, 21, 25, 26, 27
    Section 15.6:   1, 5, 8, 11, 16, 19, 21, 24, 33, 35, 36, 39
    Section 15.7:   3, 8, 11, 14, 17, 20, 28, 29, 30, 34, 38, 39
    Section 15.8:   1, 2, 3, 4, 8, 9, 13, 17, 20, 23, 26, 27
    Section 15.9:   1, 4, 6, 7, 12, 13, 15, 17, 25, 26, 27, 29

Chapter 16

    Section 16.2:   1, 3, 4, 5, 6, 10, 11, 14
    Section 16.3:   3, 5, 7, 10, 11, 14, 16, 17, 19, 22, 23, 25,29, 31, 32, 35, 37, 38, 41, 47, 49
    Section 16.4:   1, 4, 5, 7, 8, 9, 11, 13, 14, 19, 20, 23, 24, 27, 28, 29, 30
    Section 16.5:   1, 3, 6, 7, 29, 31
    Section 16.6:   1, 2
    Section 16.7:   3, 4, 5, 7, 8, 9, 13, 14, 15, 23, 24, 27, 28, 35, 44, 45, 48, 51, 52, 53
    Section 16.8:   8, 9, 10, 11, 12, 15, 16, 17, 19, 22, 23, 25, 35, 36, 37
    Section 16.9:   3, 4, 7, 8, 15, 16, 18, 19, 20, 21, 23, 25, 26, 34
    Section 16.10: 3, 4, 8, 13, 16

Chapter 17

    Section 17.1:   1, 3, 4, 5, 7, 9, 10, 11, 13, 17, 19, 22, 25, 27
    Section 17.2:   3, 4, 7, 10, 12, 14, 17, 19, 21, 23
    Section 17.4:   5, 6, 7, 8, 13, 14, 15, 16, 21, 22, 23, 24, 27, 28
    Section 17.5:   1, 3, 4, 5, 7, 9, 13, 15, 17, 19, 20, 31, 32
    Section 17.6:   2, 3, 5, 7, 11, 15, 16, 19, 22, 25, 28
    Section 17.7:   3, 6, 7, 9, 10, 18, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35
    Section 17.8:   3, 4, 6, 7, 9, 11, 13
    Section 17.9:   1, 2, 5, 6, 9, 11, 15
    Section 17.10:  2, 3, 5, 6, 9, 13, 15

 

CSD 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  The Center for Students with DisABILITIES (CSD)  website at  http://www.uh.edu/csd/  for more information.

Accommodation Forms: Students seeking academic adjustments/auxiliary aids must, in a timely manner (usually at the beginning of the semester), provide their instructor with a current Student Accommodation Form (SAF) (paper copy or  online  version, as appropriate) from the CSD office before an approved accommodation can be implemented.

Details of this policy, and the corresponding responsibilities of the student are outlined in  The Student Academic Adjustments/Auxiliary Aids Policy (01.D.09)  document under [STEP 4: Student Submission (5.4.1 & 5.4.2), Page 6]. For more information please visit the  Center for Students with Disabilities Student Resources  page.

Additionally, if a student is requesting a (CSD approved) testing accommodation, then the student will also complete a Request for Individualized Testing Accommodations (RITA) paper form to arrange for tests to be administered at the CSD office. CSD suggests that the student meet with their instructor during office hours and/or make an appointment to complete the RITA form to ensure confidentiality.

*Note: RITA forms must be completed at least 48 hours in advance of the original test date. Please consult your  counselor  ahead of time to ensure that your tests are scheduled in a timely manner. Please keep in mind that if you run over the agreed upon time limit for your exam, you will be penalized in proportion to the amount of extra time taken.

 

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.