Roberto's Math Notes
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Calculus
Prerequisites for Calculus
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Prerequisite algebra and geometry formulae
1 Algebra
2 Functions
3 Transcendental functions
4 Special functions
Differential calculus
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1 Limits and continuity
2 Resolving indeterminate forms
3 Definition of derivative
4 Basic differentiation rules
5 Derivatives of transcendental functions
6 Derivatives of other types of functions
7 Linear approximation methods
8 Graphical analysis
9 Word problems
Integral calculus
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1: Indefinite integrals
2: Integration methods
3: Basics of ODE's
4: Definite integrals and the FTC
5: Basic applications of integration
6: Improper and approximate integration
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Basic differentiation and integration formulae
Infinite series
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1: Sequences and series
2: Convergence tests
3: Power series
Linear Algebra
1: Geometric vectors
2: Euclidean vectors
3: Linear systems and matrices
4: Matrix algebra
5: Determinants
6: Lines, planes and other straight objects
7: Subspaces
8: Linear transformations
9: Orthogonality
10: Eigenvalues and diagonalization
11: Complex numbers
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Other calculus sites
Chapter 6:
Improper and approximate integration
Written Notes
6-1:
Improper integrals
6-2:
Improper integrals with one issue at one limit
6-3:
Improper integrals with one discontinuity between the limits
6-4:
Improper integrals with several improper features
6-5:
Approximate integration: the midpoint method
6-6:
Approximate integration: the trapezoid method
6-7:
Approximate integration: Simpson's method
6-8:
Comparing approximate integration methods
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