Calculus: Single and Multivariable 8th Edition By Deborah Hughes Hallett, Andrew M. Gleason
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Calculus: Single and Multivariable 8th Edition By Deborah Hughes Hallett, Andrew M. Gleason

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1,242
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38.6 MB
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eBook[PDF]
About this ebook
Calculus: Single and Multivariable, 8th Edition by Deborah Hughes-Hallett, Andrew M. Gleason, et al. (the Harvard Consortium) covers foundational single-variable calculus through advanced multivariable and vector calculus, emphasizing the "Rule of Four" (visualizing concepts graphically, numerically, symbolically, and verbally) with practical applications in engineering, science, and economics. [1, 2, 3, 4]
Core Single-Variable Topics
  • A-Review of Functions & Change: Linear, exponential, logarithmic, trigonometric, and power functions; measuring average and instantaneous speed/change; introduction to limits and continuity. [1]
  • The Derivative: Concept of the derivative, local linearity, derivative as a rate of change, interpretation functions, shortcuts (power, product, quotient, chain rules), and derivatives of trigonometric/exponential/logarithmic functions. [1]
  • Shortcuts to Differentiation & Applications: Implicit differentiation, related rates, optimization, l'Hôpital's rule, parametric equations, and the Second Derivative Test. [1]
  • The Definite Integral: Riemann sums, interpretation of the definite integral (area, accumulation), Fundamental Theorem of Calculus, and average value of a function. [1]
  • Constructing Antiderivatives & Techniques: Integration by substitution, integration by parts, partial fractions, numerical integration, and improper integrals. [1]
  • Applications of Integration: Geometry (areas, volumes, arc length), economics (consumer/producer surplus, present value), and physical/biological sciences (work, mass, probability distributions).
  • Approximation & Series: Taylor polynomials, Taylor series, power series, convergence tests (ratio, root, comparison), and Fourier series basics.
  • Differential Equations: Separation of variables, slope fields, Euler's method, and applications (logistic growth, systems).
Core Multivariable & Vector Topics
  • Functions of Several Variables: Understanding surfaces, contour diagrams (level curves), and partial derivatives.
  • A-rate of Change & Optimization: Gradient vectors, directional derivatives, tangent planes, local maxima/minima, and Lagrange multipliers.
  • Multiple Integration: Double and triple integrals, polar, cylindrical, and spherical coordinates, applications to mass, volume, and center of mass.
  • Vector Calculus: Vector fields, line integrals, flux integrals, Green’s theorem, Stokes’ theorem, and the Divergence Theorem. [1, 2]

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Topics

A-rate of Change & Optimization Applications of Integration: Geometry economics physical/biological science Approximation & Series: Taylor polynomials Taylor series power series convergence tests Constructing Antiderivatives & Techniques: Integration by substitution Core Multivariable & Vector Topics flux integrals Green’s theorem Fourier series basics. Functions & Change: Linear exponential logarithmic trigonometric and power functions; Functions of Several Variables ifferential Equations: Separation of variables Multiple Integration: Double and triple integrals Shortcuts to Differentiation & Applications: Implicit differentiation Stokes’ theorem and the Divergence Theorem The Definite Integral: Riemann sums The Derivative: Concept of the derivative local linearity derivative as a rate of change Vector Calculus: Vector fields line integrals
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