Math 1296

Mathematics & Statistics Department

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Math 1296: Calculus I

Credits: 5

Prerequisites: Math ACT 27 or higher or a grade of at least C- in Math 1250 or department consent; Credit will not be granted if credit has been received for: 1290, 1596

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 first part of a standard introduction to calculus of functions of a single variable. It includes limits, continuity, derivatives, integrals, and their applications.

Text: Calculus, 8E Early Transcendentals, James Stewart, 2016.

Course Content:




1 Functions and Models

1.1 Four Ways to Represent a Function*

1.2 Mathematical Models*

1.3 New Functions from Old Functions*

1.4 Exponential Functions*

1.5 Inverse Functions and Logarithms*

*This chapter should be a review and sections are optional.

2 Limits and Derivatives

2.1 Tangent and Velocity Problems

2.2 The Limit of a Function

2.3 Calculating Limits Using the Limit Laws

2.4 The Precise Definition of a Limit

2.5 Continuity

2.6 Limits at Infinity; Horizontal Asymptotes

2.7 Derivatives and Rates of Change

2.8 The Derivative as a Function


3 Differentiation Rules

3.1 Derivatives of Polynomials and Exponential Functions

3.2 The Product and Quotient Rules

3.3 Derivatives of Trigonometric Functions

3.4 The Chain Rule

3.5 Implicit Differentiation

3.6 Derivatives of Logarithmic Functions

3.7 Rates of Change in the Natural and Social Sciences*

3.9 Related Rates

3.10 Linear Approximations and Differentials

3.11 Hyperbolic Functions

*Note that 3.8 is not included, and 3.7 is an optional section.


4 Applications of Differentiation

4.1 Maximum and Minimum Values

4.2 The Mean Value Theorem

4.3 How do Derivatives Affect the Shape of a Graph

4.4 Indeterminate Forms and L’Hospital’s Rule

4.5 Summary of Curve Sketching

4.7 Optimization

4.9 Antiderivatives


5 Integrals

5.1 Areas and Distances

5.2 The Definite Integral

5.3 The Fundamental Theorem of Calculus

5.4 Indefinite Integrals and the Net Change Theorem

5.5 The Substitution Rule

6 Integrals

6.1 Area Between Curves

6.2 Volumes

6.3 Volumes by Cylindrical Shells*

6.4 Work*

*Sections 6.3 and 6.4 are optional.


7 Techniques of Integration

7.1 Integration by Parts