Math 1297 Calculus II

Credits: 5

Prerequisites: SP–1290 or 1296; QP–1296, 1297

Grading: A-F only

Liberal Education Category:
Category Satisfied: CATEGORY TWO: Math, Logic and Critical Thinking
Liberal Education Goals and Objectives: By the end of the term, the successful student will understand the important role that calculus plays in modeling real-world phenomena and how to apply calculus to problems in his/her discipline. Business, economics, biology, geology, chemistry, physics, engineering and numerous other disciplines make heavy use of calculus. Whenever numerical quantities change with respect to time or with respect to other variables, calculus is probably involved. The incredible success of the physical sciences and engineering in today's world is largely due to "the unreasonable effectiveness of mathematics," and calculus plays a major role in that effectiveness! The biological social and managerial scientists today also make tremendous use of calculus to solve their problems.

Course Description:
This course covers the second part of a standard introduction to calculus. It in includes discussion of vectors, applications of integrals, transcendental functions, series, and multivariable functions and partial derivatives.

Text: Calculus, 3rd Edition by Robert Smith and Roland Minton, 2008.

Course Content:

Chapter

Section

11 Vectors and the Geometry of Space

11.1 Vectors in the Plane
11.2 Vectors in Space
11.3 The Dot Product

11.4 The Cross Product
11.5 Lines and Planes in Space
11.6 Surfaces in Space

6 Exponentials, Logarithms and Other Transcendental Functions

6.1 The Natural Logarithm

6.2 Inverse Functions
6.3 The Exponential Function
6.4 Inverse Trigonometric Functions
6.5 The Calculus of Inverse Trigonometric Functions
6.6 Hyperbolic Functions.

 

7 Integration Techniques

7.1 Review of Formulas and Techniques
(7.2 Covered in Math 1296)

7.3 Trigonometric Integrals
7.4 Integration of Rational Functions using Partial Fractions
7.5 Integration Using Tables

7.6 Indeterminate Forms and L'Hospital's Rule

9 Infinite Series

9.1 Sequences of Real Numbers
9.2 Infinite Series
9.3 The Integral Test and Comparison Tests
9.4 Alternating Series
9.5 Absolute Convergence and the Ratio and Root Tests
9.6 Power Series
9.7 Taylor Series
9.8 Applications of Taylor Polynomials

9.9 Fourier Series **

 

13 Partial Derivatives

13.1 Functions of Several Variables
13.2 Limits and Continuity
13.3 Partial Derivatives
13.4 Tangent Planes and Linear Approximations

13.5 The Chain Rule

 

 

** Included as time permit

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