# Math 265 - Calculus III

## Course Coordinator

Elgin Johnston (ehjohnst@iastate.edu)

## Catalog Description

MATH 265. Calculus III.

(4-0) Cr. 4. F.S.SS. Prereq: Minimum of C- in MATH 166 or MATH 166H
Analytic geometry and vectors, differential calculus of functions of several variables, multiple integrals, vector calculus.

## Textbook Weir/Hass
Thomas' Calculus, Early Transcendentals, Twelfth Edition.
Pearson Publishing
ISBN: 9780321587992

## Syllabus

Chapter and Section references are to Thomas' Calculus, Early Transcendentals, 12th ed.

Times are suggested based on a 15-week semester of 59 class meetings, allowing 8 days for review and exams.

Chapter & Sections Topics Time
Chapter 12 - Vectors and the Geometry of Space 8 days
§§12.1-6
Chapter 13 - Vector-Valued Functions and Motion in Space 7 days
§§13.1-5
§13.6 (optional)

Chapter 14 - Partial Derivatives 12 days
§§14.1-8
§14.9 (optional)

Chapter 15 - Multiple Integrals 10 days
§§15.1-7
Chapter 16 - Integration in Vector Fields 14 days
§§16.1-8

## Objectives

### Geometry in Space, Vectors

• Use the parallelogram law to add geometric vectors.
Resolve geometric vectors into components parallel to coordinate axes.
• Perform the operations of vector addition and scalar multiplication, and interpret them geometrically.
• Use the dot product to calculate magnitude of a vector, angle between vectors,
and projection of one vector on another.
• Find and use direction angles and direction cosines of a vector.
• Use parametric equations for plane curves and space curves.
• Use and convert between parametric and symmetric equations for a straight line.
• Find a tangent line at a point on a parametric curve; compute the length of a parametric curve.
• Compute velocity, unit tangent and acceleration vectors along a parametric curve;
resolve acceleration into tangential and normal components and compute curvature.
• Use and interpret geometrically the standard equation for a plane.
• Use the cross product; interpret the cross product geometrically and as area of a parallelogram;
interpret the vector triple product as volume of a parallelepiped.
• Recognize cylinders and quadric surfaces from their Cartesian equations.
• Use cylindrical and spherical coordinates, and convert among these two and rectangular coordinates.

### Derivatives for Functions of Two or More Variables

• Represent a function of two variables as the graph of a surface; sketch level curves.
• Calculate partial derivatives and the gradient.
• Use the gradient to find tangent planes, directional derivatives and linear approximations.
Interpret the gradient geometrically.
• Use the Chain Rule.
• Find and classify critical points of functions of two variables, using the second derivative test.
• Use Lagrange's method to maximize or minimize a function subject to constraints.
• Find maximum and minimum values for a function defined on a closed, bounded, planar set.

### Multiple Integrals

• State the definition of the integral of a function over a rectangle.
• Use iterated integrals to evaluate integrals over planar regions, and to calculate volume.
• Build on elementary integration techniques to evaluate multiple integrals efficiently.
• Set up and evaluate double integrals in polar coordinates.
• Set up and evaluate integrals to compute surface area.
• Set up and evaluate triple integrals in Cartesian coordinates.
• Use double and triple integrals to compute moments, center of mass, and moments of inertia.
• Use cylindrical and spherical coordinates; change coordinates from
rectangular to cylindrical or spherical or the reverse.
• Set up and evaluate triple integrals in cylindrical and spherical coordinates.
• Change the order of variables in multiple integrals.
• Carry out change of variables in multiple integrals.

### Vector Calculus

• Calculate the curl and divergence of a vector field.
• Set up and evaluate line integrals of scalar functions or vector fields along curves.
• Recognize conservative vector fields, and apply the fundamental
theorem for line integrals of conservative vector fields.
• State and apply Green's Theorem.
• Set up and evaluate surface integrals; compute surface area and
the flux of a vector field through a surface.
• Set up and evaluate integrals over parametric surfaces.
• State and apply the Divergence Theorem.
• State and apply Stokes' Theorem.

## Old Exams

There are no common Midterm Exams
Final Fall 2014
Final Spring 2015
Final Fall 2015

## Official Math Department Policies

The Math Department Class Policies page describes the official policies that all instructors have to follow. It covers rules on make-up exams, cheating, student behavior, etc.

## Students With Disabilities

If you have a documented disability and require accommodations, you should obtain a Student Academic Accommodation Request (SAAR) from the Disability Resources office (Student Services Building, Room 1076, 294-6624 or TDD 294-6335, disabilityresources@iastate.edu or accommodations@iastate.edu). Please contact your instructor early in the semester so that your learning needs may be appropriately met.

More information about disability resources in the Mathematics Department can be found at http://www.math.iastate.edu/Undergrad/AccommodationPol.html.