Course Content
UNIT 1: Functions
-
1.1 Functions and Their Graphs
-
1.2 Combining Functions; Shifting and Scaling Graphs
-
1.3 Trigonometric Functions
-
1.4 Graphing with Calculators and Computers
-
1.5 Exponential Functions
-
1.6 Inverse Functions and Logarithms
UNIT 2: Limits and Continuity
-
2.1 Rates of Change and Tangents to Curves
-
2.2 Limit of a Function and Limit Laws
-
2.3 The Precise Definition of a Limit
-
2.4 One-Sided Limits
-
2.5 Continuity
-
2.6 Limits Involving Infinity; Asymptotes of Graphs
UNIT 3: Differentiation
-
3.1 Tangents and the Derivative at a Point
-
3.2 The Derivative as a Function
-
3.3 Differentiation Rules 135
-
3.4 The Derivative as a Rate of Change
-
3.5 Derivatives of Trigonometric Functions
-
3.6 The Chain Rule
-
3.7 Implicit Differentiation
-
3.8 Derivatives of Inverse Functions and Logarithms
-
3.9 Inverse Trigonometric Functions
-
3.10 Related Rates
-
3.11 Linearization and Differentials
UNIT 4: Applications of Derivatives
-
4.1Extreme Values of Functions
-
4.2 Monotonic Functions and the First Derivative Test
-
4.3 The Mean Value Theorem
-
4.4 Concavity and Curve Sketching
-
4.5 Indeterminate Forms and L’Hôpital’s Rule
-
4.6 Applied Optimization
-
4.7 Newton’s Method
-
4.8 Antiderivatives
UNIT 5: Integration
-
5.1 Area and Estimating with Finite Sums
-
5.2 Sigma Notation and Limits of Finite Sums
-
5.3 The Definite Integral
-
5.4 The Fundamental Theorem of Calculus
-
5.5 Indefinite Integrals and the Substitution Method
-
5.6 Substitution and Area Between Curves
UNIT 6: Applications of Definite Integrals
-
6.1 Volumes Using Cross-Sections
-
6.2 Volumes Using Cylindrical Shells
-
6.3 Arc Length
-
6.4 Areas of Surfaces of Revolution
-
6.5 Work and Fluid Forces
-
6.6 Moments and Centers of Mass
UNIT 7: Integrals and Transcendental Functions
-
7.1 The Logarithm Defined as an Integral
-
7.2 Exponential Change and Separable Differential Equations
-
7.3 Hyperbolic Functions
-
7.4 Relative Rates of Growth
UNIT 8: Techniques of Integration
-
8.1 Integration by Parts
-
8.2 Trigonometric Integrals
-
8.3 Trigonometric Substitutions
-
8.4 Integration of Rational Functions by Partial Fractions
-
8.5 Integral Tables and Computer Algebra Systems
-
8.6 Numerical Integration
-
8.7 Improper Integrals
UNIT 9: First-Order Differential Equations
-
9.1 Solutions, Slope Fields, and Euler’s Method
-
9.2 First-Order Linear Equations
-
9.3 Applications
-
9.4 Graphical Solutions of Autonomous Equations
-
9.5 Systems of Equations and Phase Planes
UNIT 10: Infinite Sequences and Series
-
10.1 Sequences
-
10.2 Infinite Series
-
10.3 The Integral Test
-
10.4 Comparison Tests
-
10.5 The Ratio and Root Test
-
10.6 Alternating Series, Absolute and Conditional Convergence
-
10.7 Power Series
-
10.8 Taylor and Maclaurin Series
-
10.9 Convergence of Taylor Series
-
10.10 The Binomial Series and Applications of Taylor Series
UNIT 11: Parametric Equations and Polar Coordinates
-
11.1 Parametrizations of Plane Curves
-
11.2 Calculus with Parametric Curves
-
11.3 Polar Coordinates
-
11.4 Graphing in Polar Coordinates
-
11.5 Areas and Lengths in Polar Coordinates
-
11.6 Conic Sections
-
11.7 Conics in Polar Coordinates
UNIT 12: Vectors and the Geometry of Space
-
12.1 Three-Dimensional Coordinate Systems
-
12.2 Vectors
-
12.3 The Dot Product
-
12.4 The Cross Product
-
12.5 Lines and Planes in Space
-
12.6 Cylinders and Quadric Surfaces
UNIT 13: Vector-Valued Functions and Motion in Space
-
13.1 Curves in Space and Their Tangents
-
13.2 Integrals of Vector Functions; Projectile Motion
-
13.3 Arc Length in Space
-
13.4 Curvature and Normal Vectors of a Curve
-
13.5 Tangential and Normal Components of Acceleration
-
13.6 Velocity and Acceleration in Polar Coordinates
UNIT 14 Partial Derivatives
-
14.1 Functions of Several Variables
-
14.2 Limits and Continuity in Higher Dimensions
-
14.3 Partial Derivatives
-
14.4 The Chain Rule
-
14.5 Directional Derivatives and Gradient Vectors
-
14.6 Tangent Planes and Differentials
-
14.7 Extreme Values and Saddle Points
-
14.8 Lagrange Multipliers
-
14.9 Taylor’s Formula for Two Variables
-
14.10 Partial Derivatives with Constrained Variables
UNIT 15: Multiple Integrals
-
15.1 Double and Iterated Integrals over Rectangles
-
15.2 Double Integrals over General Regions
-
15.3 Area by Double Integration
-
15.4 Double Integrals in Polar Form
-
15.5 Triple Integrals in Rectangular Coordinates
-
15.6 Moments and Centers of Mass
-
15.7 Triple Integrals in Cylindrical and Spherical Coordinates
-
15.8 Substitutions in Multiple Integrals
UNIT 16: Integration in Vector Fields
-
16.1 Line Integrals
-
16.2 Vector Fields and Line Integrals: Work, Circulation, and Flux
-
16.3 Path Independence, Conservative Fields, and Potential Functions
-
16.4 Green’s Theorem in the Plane
-
16.5 Surfaces and Area
-
16.6 Surface Integrals
-
16.6 Surface Integrals
-
16.7 Stokes’ Theorem
-
16.8 The Divergence Theorem and a Unified Theory
UNIT 17: Second-Order Differential Equations
-
17.1 Second-Order Linear Equations
-
17.2 Nonhomogeneous Linear Equations
-
17.3 Applications
-
17.4 Euler Equations
-
17.5 Power Series Solutions
Appendices
-
A.1 Real Numbers and the Real Line
-
A.2 Mathematical Induction
-
A.3 Lines, Circles, and Parabolas
-
A.4 Proofs of Limit Theorems
-
A.5 Commonly Occurring Limits
-
A.6 Theory of the Real Numbers
-
A.7 Complex Numbers
-
A.8 The Distributive Law for Vector Cross Products
-
A.9 The Mixed Derivative Theorem and the Increment Theorem
Student Ratings & Reviews
No Review Yet
admin
