Calculus

This general calculus book covers a fairly standard course sequence: single variable calculus, infinite series, and multivariable calculus.

Calculus Mathematics

Tác giả: David Guichard
Nhà xuất bản: Whitman College
Nguồn: LibreTexts
Giấy phép: CC BY-NC-SA
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

Đọc trực tuyến Tải PDF (nguồn mở)

Mục lục· 146 mục

01: Analytic Geometry
1.01: Prelude to Analytic Geometry
1.02: Lines
1.03: Distance Between Two Points Circles
1.04: Functions
1.05: Shifts and Dilations
1.E: Analytic Geometry (Exercises)
02: Instantaneous Rate of Change- The Derivative
2.01: The Slope of a Function
2.02: An Example
2.03: Limits
2.04: The Derivative Function
2.05: Adjectives for Functions
2.E: Instantaneous Rate of Change- The Derivative (Exercises)
03: Rules for Finding Derivatives
3.01: The Power Rule
3.02: Linearity of the Derivative
3.03: The Product Rule
3.04: The Quotient Rule
3.05: The Chain Rule
3.E: Rules for Finding Derivatives (Exercises)
04: Transcendental Functions
4.01: Trigonometric Functions
4.02: The Derivative of 1 sin x
4.03: A Hard Limit
4.04: The Derivative of sin x - II
4.05: Derivatives of the Trigonometric Functions
4.06: Exponential and Logarithmic Functions
4.07: Derivatives of the Exponential and Logarithmic Functions
4.08: Implicit Differentiation
4.09: Inverse Trigonometric Functions
4.10: Limits Revisited
4.11: Hyperbolic Functions
4.E: Transcendental Functions (Exercises)
05: Curve Sketching
5.01: Maxima and Minima
5.02: The First Derivative Test
5.03: The Second Derivative Test
5.04: Concavity and Inflection Points
5.05: Asymptotes and Other Things to Look For
5.E: Curve Sketching (Exercises)
06: Applications of the Derivative
6.01: Optimization
6.02: Related Rates
6.03: Newton's Method
6.04: Linear Approximations
6.05: The Mean Value Theorem
6.E: Applications of the Derivative (Exercises)
07: Integration
7.01: Two Examples
7.02: The Fundamental Theorem of Calculus
7.03: Some Properties of Integrals
7.E: Integration (Exercises)
08: Techniques of Integration
8.01: Prelude to Techniques of Integration
8.02: u-Substitution
8.03: Powers of sine and cosine
8.04: Trigonometric Substitutions
8.05: Integration by Parts
8.06: Rational Functions
8.07: Numerical Integration
8.E: Techniques of Integration (Exercises)
09: Applications of Integration
9.01: Area Between Curves
9.02: Distance Velocity and Acceleration
9.03: Volume
9.04: Average Value of a Function
9.05: Work
9.06: Center of Mass
9.07: Kinetic energy and Improper Integrals
9.08: Probability
9.09: Arc Length
9.10: Surface Area
9.E: Applications of Integration (Exercises)
10: Polar Coordinates and Parametric Equations
10.01: Polar Coordinates
10.02: Slopes in Polar Coordinates
10.03: Areas in Polar Coordinates
10.04: Parametric Equations
10.05: Calculus with Parametric Equations
10.E: Polar Coordinates Parametric Equations (Exercises)
11: Sequences and Series
11.01: Prelude to Sequences and Series
11.02: Sequences
11.03: Series
11.04: The Integral Test
11.05: Alternating Series
11.06: Comparison Test
11.07: Absolute Convergence
11.08: The Ratio and Root Tests
11.09: Power Series
11.10: Calculus with Power Series
11.11: Taylor Series
11.12: Taylor's Theorem
11.13: Additional Exercises
11.E: Sequences and Series (Exercises)
12: Three Dimensions
12.01: The Coordinate System
12.02: Vectors
12.03: The Dot Product
12.04: The Cross Product
12.05: Lines and Planes
12.06: Other Coordinate Systems
12.E: Three Dimensions (Exercises)
13: Vector Functions
13.01: Space Curves
13.02: Calculus with Vector Functions
13.03: Arc length and Curvature
13.04: Motion Along a Curve
13.05: Vector Functions (Exercises)
14: Partial Differentiation
14.01: Functions of Several Variables
14.02: Limits and Continuity
14.03: Partial Differentiation
14.04: The Chain Rule
14.05: Directional Derivatives
14.06: Higher order Derivatives
14.07: Maxima and minima
14.08: Lagrange Multipliers
14.E: Partial Differentiation (Exercises)
15: Multiple Integration
15.01: Volume and Average Height
15.02: Double Integrals in Cylindrical Coordinates
15.03: Moment and Center of Mass
15.04: Surface Area
15.05: Triple Integrals
15.06: Cylindrical and Spherical Coordinates
15.07: Change of Variables
16: Vector Calculus
16.01: Vector Fields
16.02: Line Integrals
16.03: The Fundamental Theorem of Line Integrals
16.04: Green's Theorem
16.05: Divergence and Curl
16.06: Vector Functions for Surfaces
16.07: Surface Integrals
16.08: Stokes's Theorem
16.09: The Divergence Theorem
17: Differential Equations
17.01: First Order Differential Equations
17.02: First Order Homogeneous Linear Equations
17.03: First Order Linear Equations
17.04: Approximation
17.05: Second Order Homogeneous Equations
17.06: Second Order Linear Equations
17.07: Second Order Linear Equations II