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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/jantz.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
Morning Class Schedule: 8:15 – 11:00 a.m.
Afternoon Class Schedule: 12:30 – 3:15 p.m.
Requirements: Three Ring Binder
Loose Leaf Paper and Pencils
Graphing Calculator
Grade Determination: 20% - Assignments
20% - Quizzes
40% - Tests
20% - Final (3 hours)
Sections
and Topics Covered:
0.1 Real Numbers, Estimation, and
Logic
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
Sections
and Topics Covered:
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
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