Math 221 Calculus 1

A first course in the calculus of single-variable functions. This course focuses on limits and derivatives, and introduces integrals.

Mathematics

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Nguồn: LibreTexts
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

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01: Functions and Graphs
1.01: Prelude to Functions and Graphs
1.02: Review of Functions
1.2E: Exercises for Section 1.2
1.03: Basic Classes of Functions
1.3E: Exercises for Section 1.3
1.04: Trigonometric Functions
1.4E: Exercises for Section 1.4
1.05: Inverse Functions
1.5E: Exercises for Section 1.5
1.06: Exponential and Logarithmic Functions
1.6E: Exercises for Section 1.6
1.07: Chapter 1 Review Exercises
02: Limits
2.01: Prelude to Limits
2.02: A Preview of Calculus
2.2E: Exercises for Section 2.2
2.03: The Limit of a Function
2.3E: Exercises for Section 2.3
2.04: The Limit Laws
2.4E: Exercises for Section 2.4
2.05: Continuity
2.5E: Exercises for Section 2.5
2.06: The Precise Definition of a Limit
2.6E: Exercises for Section 2.6
2.07: Chapter 2 Review Exercises
03: Derivatives
3.01: Prelude to Derivatives
3.02: Defining the Derivative
3.2E: Exercises for Section 3.2
3.03: The Derivative as a Function
3.3E: Exercises for Section 3.3
3.04: Differentiation Rules
3.4E: Exercises for Section 3.4
3.05: Derivatives as Rates of Change
3.5E: Exercises for Section 3.5
3.06: Derivatives of Trigonometric Functions
3.6E: Exercises for Section 3.6
3.07: The Chain Rule
3.7E: Exercises for Section 3.7
3.08: Derivatives of Inverse Functions
3.8E: Exercises for Section 3.8
3.09: Implicit Differentiation
3.9E: Exercises for Section 3.9
3.10: Derivatives of Exponential and Logarithmic Functions
3.10E: Exercises for Section 3.10
3.11: Chapter 3 Review Exercises
04: Applications of Derivatives
4.01: Prelude to Applications of Derivatives
4.02: Related Rates
4.2E: Exercises for Section 4.2
4.03: Linear Approximations and Differentials
4.3E: Exercises for Section 4.3
4.04: Maxima and Minima
4.4E: Exercises for Section 4.4
4.05: The Mean Value Theorem
4.5E: Exercises for Section 4.5
4.06: Derivatives and the Shape of a Graph
4.6E: Exercises for Section 4.6
4.07: Limits at Infinity and Asymptotes
4.7E: Exercises for Section 4.7
4.08: Applied Optimization Problems
4.8E: Exercises for Section 4.8
4.09: LHopitals Rule
4.9E: Exercises for Section 4.9
4.10: Newtons Method
4.10E: Exercises for Section 4.10
4.11: Antiderivatives
4.11E: Exercises for Section 4.11
4.12: Chapter 4 Review Exercises
05: Integration
5.01: Approximating Areas
5.1E: Exercises for Section 5.1
5.02: The Definite Integral
5.2E: Exercises for Section 5.2
5.03: The Fundamental Theorem of Calculus
5.3E: Exercises for Section 5.3
5.04: Integration Formulas and the Net Change Theorem
5.4E: Exercises for Section 5.4
5.05: Substitution
5.5E: Exercises for Section 5.5
5.06: Integrals Involving Exponential and Logarithmic Functions
5.6E: Exercises for Section 5.6
5.07: Integrals Resulting in Inverse Trigonometric Functions
5.7E: Exercises for Section 5.7
5.08: Chapter 5 Review Exercises
06: Applications of Integration
6.01: Prelude to Applications of Integration
6.02: Areas between Curves
6.2E: Exercises for Section 6.1
6.03: Determining Volumes by Slicing
6.3E: Exercises for Section 6.2
6.04: Volumes of Revolution - Cylindrical Shells
6.4E: Exercises for Section 6.3
6.05: Arc Length of a Curve and Surface Area
6.5E: Exercises for Section 6.4
6.06: Physical Applications of Integration
6.6E: Exercises for Section 6.5
6.07: Moments and Centers of Mass
6.7E: Exercises for Section 6.6
6.08: Integrals Exponential Functions and Logarithms
6.8E: Exercises for Section 6.7
6.09: Exponential Growth and Decay
6.9E: Exercises for Section 6.8
6.10: Calculus of the Hyperbolic Functions
6.10E: Exercises for Section 6.9
6.11: Chapter 6 Review Exercises
07: Appendices
7.01: A- Table of Derivatives
7.02: B- Table of Integrals