Calculus I – Fall Semester       Calculus II – Spring Semester

Instructor:  Mike Jantz

Phone: (580) 242-2750, ext. 129

E-mail:  ossmcalculus@autrytech.com

URL:  http://ossm.autrytech.com/calculus/instructors.htm  

 

Course Objectives:  To achieve college level calculus knowledge.  To receive advanced placement credit and be prepared to start Calculus II or higher in college.       

Textbook:  Calculus, 9th Edition by Varberg, Purcell, and Rigdon

Topics:  Properties and applications of  functions, limits, derivatives, integrals, polynomial approximations and series.

Semester Schedule:  We will follow the Autry Technology Center schedule.

Morning Class Schedule:  8:15 – 11:00 a.m.

Afternoon Class Schedule:  12:30 – 3:15 p.m.

Grade Determination:  20% - Assignments
                                     20% - Quizzes
                                     40% - Tests
                                     20% - Final (3 hours)

           

Calculus I – Fall 2011

Sections and Topics Covered:

0.1   Real Numbers, Estimation, and Logic

0.2   Inequalities and Absolute Values

0.3   The Rectangular Coordinate System

0.4   Graphs of Equations

0.5   Functions and Their Graphs

0.6   Operations on Functions

0.7   Trigonometric Functions

1.1   Introduction to Limits

1.2   Rigorous Study of Limits

1.3   Limit Theorems

1.6   Continuity of Functions

2.1   Two Problems with One Theme

2.2   The Derivative

2.3   Rules for Finding Derivatives

1.4   Limits Involving Trigonometric Functions

2.4   Derivatives of Trigonometric Functions

2.5   The Chain Rule

2.6   Higher-Order Derivatives

2.7   Implicit Differentiation

2.8   Related Rates

3.1   Maxima and Minima

3.2   Monotonicity and Concavity

3.3   Local Extrema and Extrema on Open Intervals

3.4   Practical Problems

1.5   Limits at Infinity; Infinite Limits

3.5   Graphing Functions Using Calculus

3.6   The Mean Value Theorem for Derivatives

3.7   Solving Equations Numerically

2.9   Differentials and Approximation

3.8   Antiderivatives

3.9   Introduction to Differential Equations

4.1   Introduction to Area

4.2   The Definite Integral

4.4   The Second Fundamental Theorem of Calculus and the Method of Substitution

4.3   The First Fundamental Theorem of Calculus

4.5   The Mean Value Theorem for Integrals and the Use of Symmetry

4.6   Numerical Integration

5.1   The Area of a Plane Region

5.2   Volumes of Solids:  Slabs, Disks, Washers

5.3   Volumes of Solids of Revolutions:  Shells

5.4   Length of a Plane Curve

5.5   Work and Fluid Force

             

Calculus II – Spring 2012

Sections and Topics Covered:

6.2   Inverse Functions and Their Derivatives

6.1   The Natural Logarithm Function

6.3   The Natural Exponential Function

6.4   General Exponential and Logarithmic Functions

6.5   Exponential Growth and Decay

6.8   The Inverse Trigonometric Functions and Their Derivatives

7.1   Basic Integration Rules

7.2   Integration by Parts

7.3   Some Trigonometric Integrals

7.4   Rationalizing Substitutions

7.5   Integration of Rational Functions Using Partial Fractions   

8.1   Indeterminate Forms of Type 0/0

8.2   Other Indeterminate Forms

8.3   Improper Integrals: Infinite Limits of Integration

8.4   Improper Integrals: Infinite Integrands

9.9   The Taylor Approximation to a Function

9.1   Infinite Sequence

9.2   Infinite Series

9.3   Positive Series:  The Integral Test

9.4   Positive Series:  Other Tests

9.5   Alternating Series, Absolute Convergence, and Conditional Convergence

9.6   Power Series

9.7   Operations on Power Series

9.8   Taylor and Maclaurin Series

10.4  Parametric Representation of Curves in the Plane

10.5  The Polar Coordinate System

10.6  Graphs of Polar Equations

10.7  Calculus in Polar Coordinates

6.6   First-Order Linear Differential Equations

6.7   Approximations for Differential Equations