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Bergen Community College
MAT 180: Precalculus
1 | Functions and Their Graphs
1.4 | Functions
1.5 | Analyzing Graphs of Functions
1.6 | A Library of Parent Functions
1.7 | Transformations of Functions
1.8 | Combinations of Functions: Composite Functions
1.9 | Inverse Functions
2 | Polynomial and Rational Functions
2.1 | Quadratic Functions and Models
2.2 | Polynomial Functions of Higher Degree
2.5 | Zeros of Polynomial Functions
2.6 | Rational Functions
2.7 | Nonlinear Inequalities
3 | Exponential and Logarithmic Functions
3.1 | Exponential Functions and Their Graphs
3.2 | Logarithmic Functions and Their Graphs
3.3 | Properties of Logarithms
3.4 | Exponential and Logarithmic Equations
3.5 | Exponential and Logarithmic Models
4 | Trigonometry
4.1 | Radian and Degree Measure
4.2 | Trigonometric Functions: The Unit Circle
4.3 | Right Triangle Trigonometry
4.4 | Trigonometric Functions of Any Angle
4.5 | Graphs of Sine and Cosine Functions
4.6 | Graphs of Other Trigonometric Functions
4.7 | Inverse Trigonometric Functions
4.8 | Applications and Models
5 | Analytic Trigonometry
5.2 | Verifying Trigonometric Identities
5.3 | Solving Trigonometric Equations
5.4 | Sum and Difference Formulas
5.5 | Multiple-Angle and Product-to-Sum Formulas
5.6 | Law of Sines
5.7 | Law of Cosines
MAT 180: The SandBox
MAT 180: Homework
MAT 180: Quizzes
MAT 180: Exams
Trigonometric Identities
Logarithmic Properties
The Unit Circle
MAT 280: Calculus I
2 | Limits and Their Properties
2.2 | Finding Limits Graphically and Numerically
2.3 | Evaluating Limits Analytically
2.4 | Continuity and One-Sided Limits
2.5 | Infinite Limits
3 | Differentiation
3.1 | The Derivative and the Tangent Line Problem
3.2 | Basic Differentiation Rules and Rates of Change
3.3 | Product and Quotient Rules and Higher-Order Derivatives
3.4 | The Chain Rule
3.5 | Implicit Differentiation
3.6 | Derivatives of Inverse Functions
3.7 | Related Rates
4 | Applications of Differentiation
4.1 | Extrema on an Interval
4.2 | Rolle’s Theorem and the Mean Value Theorem
4.3 | Increasing and Decreasing Functions and the First Derivative Test
4.4 | Concavity and the Second Derivative Test
4.5 | Limits at Infinity
4.6 | A Summary of Curve Sketching
4.7 | Optimization Problems
4.8 | Differentials
5 | Integration
5.1 | Antiderivatives and Indefinite Integration
5.2 | Area
5.3 | Riemann Sums and Definite Integrals
5.4 | The Fundamental Theorem of Calculus
5.5 | Integration by Substitution
7 | Applications of Integration
7.1 | Area of a Region Between Two Curves
MAT 280: Homework
MAT 280: Exams
MAT 280: Sandbox
MAT 280: Challenge
MAT 280: Quizzes
Differentitation Rules Reference Page
Integration Rules Reference Page
MAT 281: Calculus II
5 | Integration
5.5 | Integration by Substitution
5.6 | Numerical Integration
6 | Differential Equations
6.2 | Differential Equations: Growth and Decay
6.3 | Differential Equations: Separation of Variables
7 | Applications of Integration
7.1 | Area of a Region Between Two Curves
7.2 | Volume: The Disk Method
7.3 | Volume: The Shell Method
7.4 | Arc Length and Surfaces of Revolution
7.5 | Work
8 | Integration Techniques, L’Hospital’s Rule, and Improper Integrals
8.2 | Integration by Parts
8.3 | Trigonometric Integrals
8.4 | Trigonometric Substitution
8.5 | Partial Fractions
8.7 | Indeterminate Forms and L’Hospital’s Rule
8.8 | Improper Integrals
9 | Infinite Series
9.1 | Sequences
9.2 | Series and Convergence
9.3 | The Integral Test and p-Series
9.4 | Comparisons of Series
9.5 | Alternating Series
9.6 | The Ratio and Root Tests
9.7 | Taylor Polynomials and Approximations
9.8 | Power Series
9.9 | Representation of Functions by Power Series
9.10 | Taylor and Maclaurin Series
10 | Conics, Parametric Equations, and Polar Coordinates
10.2 | Plane Curves and Parametric Equations
10.3 | Parametric Equations and Calculus
10.4 | Polar Coordinates and Polar Graphs
10.5 | Area and Arc Length in Polar Coordinates
MAT 281: Homework
MAT 281: Challenge
MAT 281: Exams
MAT 281: Sandbox
MAT 281: Quizzes
List of Maclaurin Series for Some Common Functions
Series and Convergence Tests
Research
Graph Theory
Best monotone b-binding implies 1-factor
Stevens Institute of Technology
MA 121: Calculus IA
1 | A Library of Functions
1.6 | Powers, Polynomials, and Rational Functions
1.7 | Introduction to Continuity
1.8 | Limits
2 | Key Concept: The Derivative
2.1 | How Do We Measure Speed?
2.2 | The Derivative at a Point
2.3 | The Derivative of a Function
2.4 | Interpretations of the Derivative
2.5 | The Second Derivative
2.6 | Differentiability
3 | Short-Cuts to Differentiation
3.1 | Powers and Polynomials
3.2 | The Exponential Function
3.3 | The Product and Quotient Rules
3.4 | The Chain Rule
3.5 | The Trigonometric Functions
3.6 | The Chain Rule and Inverse Functions
3.7 | Implicit Functions
3.9 | Linear Approximation and the Derivative
4 | Using the Derivative
4.1 | Using First and Second Derivatives
4.2 | Optimization
4.3 | Optimization and Modeling
MA 121: The SandBox
MA 121: Homework
MA 121: Workshops
MA 121: Exam Review Problems
Differentiation Rules Reference Page
MA 122: Calculus IB
4 | Using the Derivative
4.7 | L’Hospitals Rule, Growth, and Dominance
5 | Key Concept: The Definite Integral
5.1 | How Do We Measure Distance Traveled?
5.2 | The Definite Integral
5.3 | The Fundamental Theorem and Interpretations
5.4 | Theorems About Definite Integrals
6 | Constructing Antiderivatives
6.1 | Antiderivatives Graphically and Numerically
6.2 | Constructing Antiderivatives Analytically
6.3 | Differential Equations and Motion
6.4 | Second Fundamental Theorem of Calculus
7 | Integration
7.1 | Integration by Substitution
7.2 | Integration by Parts
7.3 | Tables of Integrals
7.4 | Algebraic Identities and Trigonometric Substitutions
7.6 | Improper Integrals
8 | Using the Definite Integral
8.1 | Areas and Volumes
8.2 | Applications to Geometry
8.5 | Applications to Physics
8.7 | Distribution Functions
8.8 | Probability, Mean, and Median
MA 122: The SandBox
MA 122: Homework
MA 122: Workshops
MA 122: Exam Review Problems
Integration Rules Reference Page
MA 123: Calculus IIA
9 | Sequences and Series
9.2 | Geometric Series
9.3 | Convergence of Series
9.4 | Tests for Convergence
9.5 | Power Series and Interval of Convergence
10 | Approximating Functions Using Series
10.1 | Taylor Polynomials
10.2 | Taylor Series
10.3 | Finding and Using Taylor Series
10.4 | The Error in Taylor Polynomial Approximations
12 | Functions of Several Variables
12.1 | Functions of Two Variables
12.2 | Graphs and Surfaces
12.3 | Contour Diagrams
13 | A Fundamental Tool: Vectors
13.1 | Displacement Vectors
13.2 | Vectors in General
13.3 | The Dot Product
13.4 | The Cross Product
MA 123: The SandBox
MA 123: Homework
MA 123: Workshop
List of Maclaurin Series of Some Common Functions
Series Convergence Tests
Review Problems
MA 124: Calculus IIB
14 | Differentiating Functions of Several Variables
14.1 | The Partial Derivative
14.2 | Computing Partial Derivatives Algebraically
14.3 | Local Linearity and the Differential
14.4 | Gradients and Directional Derivatives in the Plane
14.5 | Gradients and Directional Derivatives in Space
14.6 | The Chain Rule
14.7 | Second-Order Partial Derivatives
15 | Optimization: Local and Global Extrema
15.1 | Critical Points: Local Extrema and Saddle Points
15.2 | Optimization
15.3 | Constrained Optimization: Lagrange Multipliers
16 | Integrating Functions of Several Variables
16.1 | The Definite Integral of a Function of Two Variables
16.2 | Iterated Integrals
16.4 | Double Integrals in Polar Coordinates
16.6 | Applications of Integration to Probability
MA 124: The SandBox
MA 124: Homework
MA 124: Workshop
Review Problems
MA 134: Discrete Math
6 | Relations
MA 221: Differential Equations
1 | Introduction
1.1 | Background
1.2 | Solutions and Initial Value Problems
1.3 | Direction Fields
1.4 | The Approximation Method of Euler
2 | First-Order Differential Equations
2.2 | Separable Equations
2.3 | Linear Equations
2.4 | Exact Solutions
2.5 | Special Integrating Factors
2.6 | Substitutions and Transformations
4 | Linear Second-Order Equations
4.1 | Introduction: The Mass-Spring Oscillator
4.2 | Homogeneous Linear Equations: The General Solution
4.3 | Auxiliary Equations with Complex Roots
4.4 | Nonhomogeneous Equations: The Method of Undetermined Coefficients
4.5 | The Superposition Principle and Undetermined Coefficients Revisited
4.6 | Variation of Parameters
6 | Theory of Higher-Order Differential Equations
6.1 | Basic Theory of Linear Differential Equations
6.2 | Homogeneous Linear Equations with Constant Coefficients
10 | Partial Differential Equations
10.4 | Fourier Cosine and Sine Series
MA 221: The SandBox
MA 221: Homework
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4.3 | Auxiliary Equations with Complex Roots