math 243: Calculus and Analytic Geometry III (4)
Course Prerequisites/Corequisites: MATH 242.
Course Description:Sequences, infinite series, conic sections, polar coordinates, two-dimensional and three-dimensional vectors, parametric equations, partial differentiation, and multiple integrals. Four hours of lecture per week.
Required Reading/Textbook: Calculus: Early Transcendentals. Sullivan and Miranda, W.H. Freemand and Company, 2nd Edition.
Learning Objectives: The student is expected to:
- learn basic properties of sequences and series, methods for determining is a sequence or a series converges and finding the limit of a convergent sequence or series, how to apply series to model and solve problems in physics, medicine and economics, and how to represent certain functions as a power series;
- learn vector notation and the vector operations for both plane and space vectors, the equations of lines, planes and surfaces in space and the applications of vectors to geometry and physics;
- learn to use vector valued functions to study motion in space; understand limits, continuity, differentiation and integration of vector valued functions and how these are used to model and solve problems in physics and astronomy;
- understand the definitions and basic properties of functions of several variables, including continuity, limits and graphs, learn the definitions and properties of derivatives of functions of several variables, including the partial derivatives, the directional derivatives, the differential and the gradient, learn the chain rules, be able to determine extrema of functions of two variables;
- learn to use multivariable functions to model problems in physics, biology, engineering, economics and agriculture and apply differentiation techniques to solve these problems, including optimization problems;
- learn the techniques for determining iterated integrals, apply these to find double and triple integrals and integrals in polar coordinates, be able to double and triple integrals to solve problems in geometry, probability, physics, engineering design, and economics;
Major Assignments/Exams
- Homework
- Quizzes
- Exams
- Final Exam
List of Discussion/Lecture Topics
- Chapter 8 INFINITE SERIES
- 8.1 Sequences
- 8.2 Infinite Series
- 8.3 Properties of Series; The Integral Test
- 8.4 Comparison Tests
- 8.5 Alternating Series; Absolute Convergence
- 8.6 Ratio Test; Root Test
- 8.7 Summary of Tests
- 8.8 Power Series
- 8.9 Taylor Series; Maclaurin Series
- Chapter 9 PARAMETRIC EQUATIONS; POLAR EQUATIONS
- 9.1 Parametric Equations
- 9.2 Tangent Lines; Arc Length
- 9.4 Polar Coordinates
- 9.5 Polar Equations
- 9.6 Area in Polar Coordinates
- Chapter 10 VECTORS
- 10.1 Rectangular Coordinates in Space
- 10.2 Introduction to Vectors
- 10.3 Vectors in the Plane and in Space
- 10.4 Dot Product
- 10.5 Cross Product
- 10.6 Equations of Lines and Planes in Space
- Chapter 11 VECTOR FUNCTIONS
- 11.1 Vector Functions and Their Derivatives
- 11.2 Unit Tangent and Normal Vectors, Arc Length
- 11.5 Integrals of Vector Functions
Chapter 12 FUNCTIONS OF SEVERAL VARIABLES
- 12.1 Functions of Two or More Variables
- 12.2 Limits and Continuity
- 12.3 Partial Derivatives
- 12.4 Differentiablility and the Differential
- 12.5 The Chain Rules
Chapter 13 DIRECTIONAL DERIVATIVES, GRADIENTS, AND EXTREMA
- 13.1 Directional Derivatives; Gradients
- 13.2 Tangent Planes
- 13.3 Extrema of Functions of Two Variables
Chapter 14 MULTIPLE INTEGRALS
- 14.1 The Double Integral over a Rectangular Region
- 14.2 The Double Integral over General Regions
- 14.3 Double Integrals Using Polar Coordinates
- 14.6 The Triple Integral
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