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Aori Nevo's Course Webpage

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  • Aori Nevo’s Course Webpage
  • 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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Review Problems

  • Exam 1 Review Problems
  • Exam 2 Review Problems
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