Math 1296 Calculus I
Credits: 5
Prerequisites: Math ACT 25 or higher or a grade of at least C- in Math 1250 or dept 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, 3rd Edition by Robert Smith and Roland Minton, 2008.
Course Content:
| Chapters | Sections |
| 1 Limits and Continuity |
1.1 A Brief Preview of Calculus: Tangent Lines and the Length of a Curve
1.2 The Concept of Limit
1.3 Computation of Limits
1.4 Continuity and Its Consequences
1.5 Limits Involving Infinity; Asymptotes
1.6 Formal Definition of the Limit
1.7 Limits and Loss-of-Significance Errors (if time permits)
|
| 2 Differentiation |
2.1 Tangent Lines and Velocity
2.2 The Derivative
2 3 Computation of Derivatives: The Power Rule
2.4 The Product and Quotient Rules
2.5 The Chain Rule
2.6 Derivatives of Trigonometric Functions
2.7 Implicit Differentiation
2.8 The Mean Value Theorem
|
| 3 Applications of Differentiation |
3.1 Linear Approximations and Newton’s Method
3.2 Maximum and Minimum Values
3.3 Increasing and Decreasing Functions
3.4 Concavity and the Second Derivative Test
3.5 Overview of Curve Sketching
3.6 Optimization
3.7 Related Rates
3.8 Rates of Change in Economics and the Sciences
|
| 4 Integration |
4.1 Antiderivatives
4.2 Sums and Sigma Notation
4.3 Area
4.4 The Definite Integral
4.5 The Fundamental Theorem of Calculus
4.6 Integration by Substitution
4.7 Numerical Integration
|
| 5 Applications of the Definite Integral |
5.1 Area Between Curves
5.2 Volume: Slicing, Disks and Washers
5.3 Volumes by Cylindrical Shells
5.4 Arc Length and Surface Area (if time permits)
5.5 Projectile Motion (if time permits)
5.6 Applications of Integration to Physics and Engineering
|
| 7 Integration Techniques |
7.2 Integration by Parts
7.7 Improper Integrals
|
