First Semester Calculus (Westphal, adapted from Open Stax)

This text is a first semester calculus text adapted from the OpenStax Calculus 1 text. Some of the material has been re-ordered; the primary change is that derivatives of exponential and log functions are covered earlier in chapter 3 than they were in the OpenStax text.

Mathematics

Tác giả: Karla Westphal
Nhà xuất bản: Saddleback College
Nguồn: LibreTexts
Giấy phép: Mixed
Ngôn ngữ: EN
Danh mục: Kế toán - Kiểm toán

Đọc trực tuyến Tải PDF (nguồn mở)

Mục lục· 97 mục

01: Functions and Graphs
1.00: Prelude to Functions and Graphs
1.01: Review of Functions
1.1E: Exercises for Section 1.1
1.02: Basic Classes of Functions
1.2E: Exercises for Section 1.2
1.03: Trigonometric Functions
1.3E: Exercises for Section 1.3
1.04: Inverse Functions
1.4E: Exercises for Section 1.4
1.05: Exponential and Logarithmic Functions
1.5E: Exercises for Section 1.5
1.R: Chapter 1 Review Exercises
02: Limits
2.00: Prelude to Limits
2.01: A Preview of Calculus
2.1.00: Examples of graphing m(x) the function that gives us the slope of a secant line in order to confirm a guess about the value of the slope of the tangent line
2.1E: Exercises for Section 2.1
2.02: The Limit of a Function
2.2E: Exercises for Section 2.2
2.03: The Limit Laws
2.3E: Exercises for Section 2.3
2.04: Continuity
2.4E: Exercises for Section 2.4
2.05: The Precise Definition of a Limit
2.5E: Exercises for Section 2.5
2.06: Limits at Infinity and Asymptotes
2.6E: Exercises for Section 2.6
2.R: Chapter 2 Review Exercises
03: Derivatives
3.00: Prelude to Derivatives
3.01: Defining the Derivative
3.1E: Exercises for Section 3.1
3.02: The Derivative as a Function
3.2E: Exercises for Section 3.2
3.03: Differentiation Rules
3.3.00: Basic differentiation rules- constants powers constant multiples sums and differences
3.3.01: Exponential functions
3.3.02: The Product and Quotient Rules
3.3E: Exercises for Section 3.3
3.04: Derivatives as Rates of Change
3.4E: Exercises for Section 3.4
3.05: Derivatives of Trigonometric Functions
3.5E: Exercises for Section 3.5
3.06: The Chain Rule
3.6.00: The Derivative of exponential functions with different bases
3.6E: Exercises for Section 3.6
3.07: Implicit Differentiation
3.7E: Exercises for Section 3.7
3.08: Derivatives of Inverse Functions
3.8.00: Preliminary examples- the derivatives of log functions
3.8.01: Derivatives of inverse functions in general and derivatives of inverse trig functions
3.8E: Exercises for Section 3.8
3.09: Reviewing exponential and logarithmic functions and introducing Logarithmic Differentiation
3.9E: Exercises for Section 3.9
3.R: Chapter 3 Review Exercises
04: Applications of Derivatives
4.00: Prelude to Applications of Derivatives
4.01: Related Rates
4.1E: Exercises for Section 4.1
4.02: Linear Approximations and Differentials
4.2E: Exercises for Section 4.2
4.03: Maxima and Minima
4.3E: Exercises for Section 4.3
4.04: The Mean Value Theorem
4.4E: Exercises for Section 4.4
4.05: Derivatives and the Shape of a Graph
4.5E: Exercises for Section 4.5
4.06: Using Calculus (and some algebra too) to graph functions
4.6E: Exercises for Section 4.6
4.07: Applied Optimization Problems
4.7E: Exercises for Section 4.7
4.08: LHopitals Rule
4.8E: Exercises for Section 4.8
4.09: Newtons Method
4.9E: Exercises for Section 4.9
4.10: Antiderivatives
4.10E: Exercises for Section 4.10
4.R: Chapter 4 Review Exercises
05: Integration
5.00: Prelude to 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: Integrals Resulting in Inverse Trigonometric Functions
5.R: Chapter 5 Review Exercises