Thomas Calculus 15th Edition By George Brinton Thomas, Joel Hass
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- Education
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About this ebook
The Thomas' Calculus, 15th Edition covers core single-variable and multivariable calculus topics across foundational and advanced STEM curricula authored by Joel Hass, Christopher Heil, and Przemyslaw Bogacki. [1, 2]
Foundational Topics (Single-Variable Calculus)
- Limits and Continuity: Rate of change, limit laws, precise definitions, and continuous functions.
- Derivatives: Derivative definition, rules of differentiation, chain rule, implicit differentiation, and related rates.
- Applications of Derivatives: Extreme values, the Mean Value Theorem, sketching graphs, optimization, and linear approximation.
- Integrals: Riemann sums, definite integrals, the Fundamental Theorem of Calculus, and substitution methods.
- Transcendental Functions: Inverse functions, exponential and logarithmic functions, natural logarithms, and inverse trigonometric functions.
- Techniques of Integration: Integration by parts, partial fractions, trigonometric substitutions, and improper integrals.
- Infinite Sequences and Series: Convergence tests, power series, Taylor and Maclaurin series.
Advanced Topics (Multivariable Calculus & Vector Calculus)
- Parametric Equations and Polar Coordinates: Graphing in polar coordinates, conic sections, and calculus with parametrized curves.
- Vectors and the Geometry of Space: Dot and cross products, lines, planes, and cylinder/quadric surfaces.
- Vector-Valued Functions: Motion in space, arc length, and unit tangent/normal vectors.
- Partial Derivatives: Functions of several variables, limits, continuity, chain rule, directional derivatives, and optimization.
- Multiple Integrals: Double and triple integrals in rectangular, cylindrical, and spherical coordinates, plus substitutions.
- Vector Calculus: Vector fields, line integrals, Green's theorem, surface integrals, Stokes' theorem, and the Divergence Theorem.
New Additions in the 15th Edition
- Determinants and Gradient Descent: A new appendix focusing on concepts for machine learning and neural networks.
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45.87 MB
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