Calculus

Calculus Mathematics

Author: Gregory Hartman et al.
Publisher: Virginia Military Institute
Source: LibreTexts
License: CC BY-NC
Language: EN
Category: Basic Sciences

Read online Download PDF (open licence)

Contents· 112 sections

01: Limits
1.01: An Introduction to Limits
1.02: Epsilon-Delta Definition of a Limit
1.03: Finding Limits Analytically
1.04: One Sided Limits
1.05: Continuity
1.06: Limits Involving Infinity
1.E: Applications of Limits (Exercises)
02: Derivatives
2.01: Instantaneous Rates of Change- The Derivative
2.02: Interpretations of the Derivative
2.03: Basic Differentiation Rules
2.04: The Product and Quotient Rules
2.05: The Chain Rule
2.06: Implicit Differentiation
2.07: Derivatives of Inverse Functions
2.E: Applications of Derivatives(Exercises)
03: The Graphical Behavior of Functions
3.01: Extreme Values
3.02: The Mean Value Theorem
3.03: Increasing and Decreasing Functions
3.04: Concavity and the Second Derivative
3.05: Curve Sketching
3.E: Applications of the Graphical Behavior of Functions(Exercises)
04: Applications of the Derivative
4.01: Newton's Method
4.02: Related Rates
4.03: Optimization
4.04: Differentials
4.E: Applications of Derivatives (Exercises)
05: Integration
5.01: Antiderivatives and Indefinite Integration
5.02: The Definite Integral
5.03: Riemann Sums
5.04: The Fundamental Theorem of Calculus
5.05: Numerical Integration
5.E: Applications of Integration (Exercises)
06: Techniques of Integration
6.01: Substitution
6.02: Integration by Parts
6.03: Trigonometric Integrals
6.04: Trigonometric Substitution
6.05: Partial Fraction Decomposition
6.06: Hyperbolic Functions
6.07: L'Hopital's Rule
6.08: Improper Integration
6.E: Applications of Antidifferentiation (Exercises)
07: Applications of Integration
7.01: Area Between Curves
7.02: Volume by Cross-Sectional Area- Disk and Washer Methods
7.03: The Shell Method
7.04: Arc Length and Surface Area
7.05: Work
7.06: Fluid Forces
7.E: Applications of Integration (Exercises)
08: Sequences and Series
8.01: Sequences
8.02: Infinite Series
8.03: Integral and Comparison Tests
8.04: Ratio and Root Tests
8.05: Alternating Series and Absolute Convergence
8.06: Power Series
8.07: Taylor Polynomials
8.08: Taylor Series
8.E: Applications of Sequences and Series (Exercises)
09: Curves in the Plane
9.01: Conic Sections
9.02: Parametric Equations
9.03: Calculus and Parametric Equations
9.04: Introduction to Polar Coordinates
9.05: Calculus and Polar Functions
9.E: Applications of Curves in a Plane (Exercises)
10: Vectors
10.01: Introduction to Cartesian Coordinates in Space
10.02: An Introduction to Vectors
10.03: The Dot Product
10.04: The Cross Product
10.05: Lines
10.06: Planes
10.E: Applications of Vectors (Exercises)
11: Vector-Valued Functions
11.01: VectorValued Functions
11.02: Calculus and Vector-Valued Functions
11.03: The Calculus of Motion
11.04: Unit Tangent and Normal Vectors
11.05: The Arc Length Parameter and Curvature
11.E: Applications of Vector Valued Functions (Exercises)
12: Functions of Several Variables
12.01: Introduction to Multivariable Functions
12.02: Limits and Continuity of Multivariable Functions
12.03: Partial Derivatives
12.04: Differentiability and the Total Differential
12.05: The Multivariable Chain Rule
12.06: Directional Derivatives
12.07: Tangent Lines Normal Lines and Tangent Planes
12.08: Extreme Values
12.E: Applications of Functions of Several Variables (Exercises)
13: Multiple Integration
13.01: Iterated Integrals and Area
13.02: Double Integration and Volume
13.03: Double Integration with Polar Coordinates
13.04: Center of Mass
13.05: Surface Area
13.06: Volume Between Surfaces and Triple Integration
13.E: Applications of Multiple Integration (Exercises)
14: Appendix
14.01: Section 1-
14.02: Section 2-
14.03: Section 3-
14.04: Section 4-
14.05: Section 5-
14.06: Section 6-