Calculus.pdf



Calculus, by Gilbert Strang, published in 1991 and still in print from Wesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. This book is available online free at MIT Open Courseware.

Contents:

  • 1: Introduction to Calculus
    • 1.1 Velocity and Distance
    • 1.2 Calculus Without Limits
    • 1.3 The Velocity at an Instant
    • 1.4 Circular Motion
    • 1.5 A Review of Trigonometry
    • 1.6 A Thousand Points of Light
    • 1.7 Computing in Calculus
  • 2: Derivatives
    • 2.1 The Derivative of a Function
    • 2.2 Powers and Polynomials
    • 2.3 The Slope and the Tangent Line
    • 2.4 Derivative of the Sine and Cosine
    • 2.5 The Product and Quotient and Power Rules
    • 2.6 Limits
    • 2.7 Continuous Functions
  • 3: Applications of the Derivative
    • 3.1 Linear Approximation
    • 3.2 Maximum and Minimum Problems
    • 3.3 Second Derivatives: Minimum vs. Maximum
    • 3.4 Graphs
    • 3.5 Ellipses, Parabolas, and Hyperbolas
    • 3.6 Iterations x[n+1] = F(x[n])
    • 3.7 Newton’s Method and Chaos
    • 3.8 The Mean Value Theorem and l’Hopital’s Rule
  • 4: The Chain Rule
    • 4.1 Derivatives by the Charin Rule
    • 4.2 Implicit Differentiation and Related Rates
    • 4.3 Inverse Functions and Their Derivatives,pp. 164-170
    • 4.4 Inverses of Trigonometric Functions
  • 5: Integrals
    • 5.1 The Idea of an Integral
    • 5.2 Antiderivatives
    • 5.3 Summation vs. Integration
    • 5.4 Indefinite Integrals and Substitutions
    • 5.5 The Definite Integral
    • 5.6 Properties of the Integral and the Average Value
    • 5.7 The Fundamental Theorem and Its Consequences
    • 5.8 Numerical Integration
  • 6: Exponentials and Logarithms
    • 6.1 An Overview
    • 6.2 The Exponential e^x
    • 6.3 Growth and Decay in Science and Economics
    • 6.4 Logarithms
    • 6.5 Separable Equations Including the Logistic Equation
    • 6.6 Powers Instead of Exponentials
    • 6.7 Hyperbolic Functions
  • 7: Techniques of Integration
    • 7.1 Integration by Parts
    • 7.2 Trigonometric Integrals
    • 7.3 Trigonometric Substitutions
    • 7.4 Partial Fractions
    • 7.5 Improper Integrals
  • 8: Applications of the Integral
    • 8.1 Areas and Volumes by Slices
    • 8.2 Length of a Plane Curve
    • 8.3 Area of a Surface of Revolution
    • 8.4 Probability and Calculus
    • 8.5 Masses and Moments
    • 8.6 Force, Work, and Energy
  • 9: Polar Coordinates and Complex Numbers
    • 9.1 Polar Coordinates
    • 9.2 Polar Equations and Graphs
    • 9.3 Slope, Length, and Area for Polar Curves
    • 9.4 Complex Numbers
  • 10: Infinite Series
    • 10.1 The Geometric Series
    • 10.2 Convergence Tests: Positive Series
    • 10.3 Convergence Tests: All Series
    • 10.4 The Taylor Series for e^x, sin x, and cos x
    • 10.5 Power Series
  • 11: Vectors and Matrices
    • 11.1 Vectors and Dot Products
    • 11.2 Planes and Projections
    • 11.3 Cross Products and Determinants
    • 11.4 Matrices and Linear Equations
    • 11.5 Linear Algebra in Three Dimensions
  • 12: Motion along a Curve
    • 12.1 The Position Vector
    • 12.2 Plane Motion: Projectiles and Cycloids
    • 12.3 Tangent Vector and Normal Vector
    • 12.4 Polar Coordinates and Planetary Motion
  • 13: Partial Derivatives
    • 13.1 Surface and Level Curves
    • 13.2 Partial Derivatives
    • 13.3 Tangent Planes and Linear Approximations
    • 13.4 Directional Derivatives and Gradients
    • 13.5 The Chain Rule
    • 13.6 Maxima, Minima, and Saddle Points
    • 13.7 Constraints and Lagrange Multipliers
  • 14: Multiple Integrals
    • 14.1 Double Integrals
    • 14.2 Changing to Better Coordinates
    • 14.3 Triple Integrals
    • 14.4 Cylindrical and Spherical Coordinates
  • 15: Vector Calculus
    • 15.1 Vector Fields
    • 15.2 Line Integrals
    • 15.3 Green’s Theorem
    • 15.4 Surface Integrals
    • 15.5 The Divergence Theorem
    • 15.6 Stokes’ Theorem and the Curl of F
  • 16: Mathematics after Calculus
    • 16.1 Linear Algebra
    • 16.2 Differential Equations
    • 16.3 Discrete Mathematics

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Comments

2 Responses to “Calculus.pdf”

  1. bassamss on November 10th, 2009 1:18 pm

    Calculus, by Gilbert Strang, published in 1991 and still in print from Wesley-Cambridge Press, the book is a useful resource for educators and self-learners alike

  2. farai mteliso on December 1st, 2009 11:58 am

    may l have all related maths books with calculus linear algebra computer science all for operations reserch and applied statistics

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