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Calculus for Computer Scientists Lecture Notes written by Maciej Paluszynski This is an other great mathematics book cover the following topics.
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FUNCTIONS AND MODELS. LIMITS. DERIVATIVES. APPLICATIONS OF DIFFERENTIATION. INTEGRALS. APPLICATIONS OF INTEGRATION. INVERSE FUNCTIONS: TECHNIQUES OF INTEGRATION. FURTHER APPLICATIONS OF INTEGRATION. DIFFERENTIAL EQUATIONS. PARAMETRIC Equations and Polar Coordinates. INFINITE SEQUENCES AND SERIES. VECTORS AND THE GEOMETRY OF SPACE. VECTOR FUNCTIONS. PARTIAL DERIVATIVES. MULTIPLE INTEGRALS. SECOND-ORDER DIFFERENTIAL EQUATIONS. Appendixes.
Functions and Limits Derivatives Inverse Functions Application of Differentiation Integrals Techniques of Integration Applications of Integration Series Parametric Equations and Polar Coordinates Vectors and The Geometry of Space Partial Derivatives Multiple Integrals Vector Calculus Appendixes
Sequences of Real Numbers Series of Real Numbers Sequences and Series of Functions Bibliography
Functions. Limits and Continuity. Differentiation. Applications of Derivatives. Integration.
The Real Number system & Finite Dimensional Cartesian Space Limits, Continuity, and Differentiation Riemann Integration Differentiation 0f Functions of Several Variables Further Topics in Integration
Calculus – FAQ Real and complex numbers Functions Sequences Series Limit of a function at a point Continuous functions The derivative Integrals Definite integral Applications of integrals Improper integrals Wallis’ and Stirling’s formulas Numerical integration Function sequences and series
polynomials and special functions The Concept of Limit Computation of Limit Continuity and its Consequences Limits Involving Infinity Tangent Lines and Velocity Computation of Derivatives Derivatives of Trigonometric Functions.
Revision Sets, Real Numbers and Inequalities Functions and Graphs Limits Differentiation Applications of Differentiation Integration Trigonometric Functions Exponential and Logarithmic Functions More Differentiation More Integration A Answers B Supplementary Notes
Numbers and Functions Derivatives (1) Limits and Continuous Functions Derivatives (2) Graph Sketching and Max-Min Problems Exponentials and Logarithms (naturally) The Integral Applications of the integral APPLICABILITY AND DEFINITIONS, VERBATIM COPYING, COPYING IN QUANTITY, MODIFICATIONS, COMBINING DOCUMENTS, COLLECTIONS OF DOCUMENTS, AGGREGATION WITH INDEPENDENT WORKS, TRANSLATION, TERMINATION, FUTURE REVISIONS OF THIS LICENSE, RELICENS
Real Numbers, Limits and continuity The Derivative General Theorems, Indeterminate forms Techniques of Integration The Definite Integral Plance Curve I Plance Curve II Analytical Geometry of three dimensions Functions of Several Variables Multiples Integrals
Sets: Language and Notation The Extended Real Line Suprema, Infima, Completeness Neighborhoods, Open Sets and Closed Sets Magnitude and Distance Limits Limits: Properties Trigonometric Functions Continuity The Intermediate Value Theorem Inverse Functions Maxima and Minima Tangents, Slopes and Derivatives Derivatives of Trigonometric Functions Differentiability and Continuity Using the Algebra of Derivatives Using the Chain Rule Proving the Algebra of Derivatives Proving the Chain Rule Using Derivatives for Extrema Local Extrema and Derivatives Mean Value Theorem The Sign of the Derivative Differentiating Inverse Functions Analyzing local extrema with higher derivatives Exp and Log Convexity L’Hospital’s Rule Integration The Fundamental Theorem of Calculus Riemann Sum Examples Integration Techniques Paths and Length Selected Solutions, Bibliography
Review Limits Derivatives Applications of Derivatives Integrals Applications of Integrals Extras
Introduction to Calculus Derivatives Applications of the Derivative The Chain Rule Integrals Exponentials and Logarithms Techniques of Integration Applications of the Integral Polar Coordinates and Complex Numbers Infinite Series Vectors and Matrices Motion along a Curve Partial Derivatives Constraints and Lagrange Multipliers Vector Calculus Mathematics after Calculus
Indefinite integrals (Primitives, Antiderivatives) Definite integrals Improper (generalized) integrals Integrals with parameters Line integrals Double integrals Triple integrals Surface integrals Gauss and Stokes formulas. Applications Some remarks on complex functions integration
0. Before Calculus 1. Limits and Continuity 2. The Derivative 3. The Derivative in Graphing and Applications 4. Integration 5. Applications of the Definite Integral in Geometry, Science and Engineering 6. Exponential, Logarithmic, and Inverse Trigonometric Functions 7. Principles of Integral Evaluation 8. Mathematical Modeling with Differential Equations 9. Infinite Series 10. Parametric and Polar Curves; Conic Sections 11. Three-Dimensional Space; Vectors 12. Vector-Valued Functions 13. Partial Derivatives 14. Multiple Integrals 15. Topics in Vector Calculus Graphing Functions Using Calculators and Computer Algebra Systems, Trigonometry Review, Solving Polynomial Equations, Mathematical Models, Selected Proofs Web Appendices, Real Numbers, Intervals, and Inequalities, Absolute Value, Coordinate Planes, Lines, and Linear Functions, Distance, Circles, and Quadratic Functions, Second-Order Linear Homogeneous Differential Equations; The Vibrating String, The Discriminant
1. Table of Standard Results 2. Methods of Integration 3. Integration of Algebraic Rational Functions 4. Integration of Trigonometric Functions 5. Integration of Irrational Functions 6. Definite Integral as the Limit of a Sum 7. Areas of Plane Regions 8. Lengths of Plane Curves 9. Volumes and Surfaces of Revolution 10. Centre of Gravity, Moment of Inertia 11. Defferential Equations of First Order and First Degree 12. Equations of First Order but not of the First Degree 13. Trajectories of a Family of Curves 14. Linear Equaions