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Calculus 1

Calculus courses carry an intimidating reputation, but it is important to note that it is the algebra within the calculus that represents most of the stumbling blocks. In Calculus I, the student primarily learns the meaning and interpretation of derivative and integration, the two concepts that are the foundations of subsequent calculus courses. Also included is the study of differential equations. The graphing calculator is used extensively.

Table of Contents

Chapter P – PREPARATION FOR CALCULUS

P.1 Graphs and Models
P.2 Linear Models and Rates of Change
P.3 Functions and Their Graphs
P.4 Fitting Models to Data

Chapter 1 – LIMITS AND THEIR PROPERTIES

1.1 A Preview of Calculus
1.2 Finding Limits Graphically and Numerically
1.3 Evaluating Limits Analytically
1.4 Continuity and One-Sided Limits
1.5 Infinite Limits

Chapter 2 – DIFFERENTIATION

2.1 The Derivative and the Tangent Line Problem
2.2 Basic Differentiation Rules and Rates of Change
2.3 The Product and Quotient Rules and Higher-Order Derivatives
2.4 The Chain Rule
2.5 Implicit Differentiation
2.6 Related Rates

Chapter 3 – APPLICATIONS OF DIFFERENTIATION

3.1 Extrema on an Interval
3.2 Rolle’s Theorem and the Mean Value Theorem
3.3 Increasing and Decreasing Functions and the First Derivative Test
3.4 Concavity and the Second Derivative Test
3.5 Limits at Infinity
3.6 A Summary of Curve Sketching
3.7 Optimization Problems
3.8 Newton’s Method
3.9 Differentials

Chapter 4 – INTEGRATION

4.1 Antiderivatives and Indefinite Integration
4.2 Area
4.3 Riemann Sums and Definite Integrals
4.4 The Fundamental Theorem of Calculus
4.5 Integration by Substitution
4.6 Numerical Integration

Chapter 5 – LOGARITHMIC, EXPONENTIAL, AND OTHER TRANSCENDENTAL FUNCTIONS

5.1 The Natural Logarithmic Function: Differentiation
5.2 The Natural Logarithmic Function: Integration
5.3 Inverse Functions
5.4 Exponential Functions: Differentiation and Integration
5.5 Bases Other than e and Applications
5.6 Inverse Trigonometric Functions: Differentiation
5.7 Inverse Trigonometric Functions: Integration
5.8 Hyperbolic Functions

Chapter 6 – DIFFERENTIAL EQUATIONS

6.1 Slope Fields and Euler’s Method
6.2 Differential Equations: Growth and Decay
6.3 Separation of Variables and the Logistic Equation
6.4 First-Order Linear Differential Equations

Sample Videos from this Course