Calculus: Tutorial Bank (Late Transcendentals) 1st edition

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• Chapter 1: Limits and Continuity
  • 1.1: Introduction to Limits
  • 1.2: Evaluating Limits Using Limit Laws
  • 1.3: Continuity
  • 1.4: Evaluating Limits at Infinity
  • 1.5: The Precise Definition of a Limit
  
  
• Chapter 2: Differentiation
  • 2.1: Rates of Change: Secant Lines and Tangent Lines
  • 2.2: The Definition of the Derivative
  • 2.3: Power and Sum Rules
  • 2.4: Product and Quotient Rules
  • 2.5: Derivatives of Trigonometric Functions
  • 2.6: The Chain Rule
  • 2.7: Implicit Differentiation
  
  
• Chapter 3: Applications of Differentiation
  • 3.1: Linearization and Differentials
  • 3.2: Extreme Values of a Function
  • 3.3: Mean Value Theorem
  • 3.4: First and Second Derivative Tests
  • 3.5: Curve Sketching
  • 3.6: Optimization
  • 3.7: Related Rates
  • 3.8: Indeterminate Forms and L'Hospital's Rule
  • 3.9: Newton's Method
  
  
• Chapter 4: Integration
  • 4.1: Antiderivatives
  • 4.2: The Indefinite Integral
  • 4.3: The Area Under a Curve and Riemann Sums
  • 4.4: The Definite Integral
  • 4.5: The Fundamental Theorem of Calculus
  
  
• Chapter 5: Inverse Functions
  • 5.1: Exponential Functions
  • 5.2: Logarithmic Functions and Logarithmic Differentiation
  • 5.3: Inverse Trigonometric Functions
  • 5.4: Hyperbolic Functions
  • 5.5: Indeterminate Forms and L'Hospital's Rule
  
  
• Chapter 6: Integration Techniques
  • 6.1: The Substitution Method
  • 6.2: Integration by Parts
  • 6.3: Trigonometric Integrals
  • 6.4: Trigonometric Substitution
  • 6.5: Partial Fractions
  • 6.6: Integration by Tables and Computer Systems
  • 6.7: Improper Integrals
  • 6.8: Numeric Integration
  
  
• Chapter 7: Applications of Integration
  • 7.1: Areas Between Curves
  • 7.2: Volumes of Solids by Slicing
  • 7.3: Volumes of Revolution: The Disk and Washer Methods
  • 7.4: Volumes of Revolution: The Shell Method
  • 7.5: Arc Length and Areas of Surfaces of Revolution
  • 7.6: Average Value of a Function
  • 7.7: Work and Fluid Force
  • 7.8: Moments and Center of Mass
  • 7.9: Probability and Random Variables
  • 7.10: Economics
  
  
• Chapter 8: Differential Equations
  • 8.1: Introduction to Differential Equations
  • 8.2: Direction Fields and Euler's Method
  • 8.3: Separable Equations
  • 8.4: Exponential Growth and Decay
  • 8.5: The Logistic Equation
  • 8.6: First-Order Linear Equations
  
  
• Chapter 9: Sequences and Series
  • 9.1: Sequences
  • 9.2: Series
  • 9.3: The Integral Test
  • 9.4: The Comparison Tests
  • 9.5: Alternating Series, Absolute Convergence, and Conditional Convergence
  • 9.6: The Ratio and Root Tests
  • 9.7: Power Series
  • 9.8: Representing Functions as Power Series
  • 9.9: Taylor and Maclaurin Series
  
  
• Chapter 10: Parametric Equations and Polar Coordinates
  • 10.1: Parametric Equations
  • 10.2: The Calculus of Parametric Equations
  • 10.3: Polar Coordinates
  • 10.4: Calculus in Polar Coordinates
  
  
• Chapter 11: Conic Sections
  • 11.1: Introduction to Conic Sections
  • 11.2: Parametrized Conic Sections
  • 11.3: Conic Sections in Polar Coordinates
  
  
• Chapter 12: Vectors
  • 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: Surfaces in Space
  
  
• Chapter 13: Vector-Valued Functions
  • 13.1: Vector-Valued Functions and Space Curves
  • 13.2: Calculus of Vector-Valued Functions
  • 13.3: Arc Length and Curvature
  • 13.4: Velocity and Acceleration
  
  
• Chapter 14: Partial Derivatives
  • 14.1: Multivariable Functions
  • 14.2: Limits and Continuity
  • 14.3: Partial Derivatives
  • 14.4: The Chain Rule
  • 14.5: Tangent Planes and Differentials
  • 14.6: Directional Derivatives and Gradients
  • 14.7: Extrema of Multivariable Functions
  • 14.8: Lagrange Multipliers
  
  
• Chapter 15: Multiple Integration
  • 15.1: Double Integrals over Rectangles
  • 15.2: Iterated Integrals
  • 15.3: Double Integrals over General Regions
  • 15.4: Double Integrals in Polar Coordinates
  • 15.5: Applications of Double Integrals
  • 15.6: Triple Integrals in Rectangular Coordinates
  • 15.7: Triple Integrals in Other Coordinate Systems
  • 15.8: Change of Variables in Multiple Integrals
  
  
• Chapter 16: Vector Calculus
  • 16.1: Vector Fields
  • 16.2: Line Integrals
  • 16.3: Path Independence and Conservative Vector Fields
  • 16.4: Green's Theorem
  • 16.5: Parametric Surfaces and Areas
  • 16.6: Surface Integrals
  • 16.7: Curl and Divergence
  • 16.8: Stokes's Theorem
  • 16.9: The Divergence Theorem
  
  
• Chapter 17: Second-Order Differential Equations
  • 17.1: Second-Order Linear Homogeneous Equations
  • 17.2: Second-Order Linear Nonhomogeneous Equations
  • 17.3: Applications of Second-Order Differential Equations
  • 17.4: Infinite Series and Differential Equations