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
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Basic differentiation and integration formulae
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
Learning support resources
Learning skills
Pre-Engineering math
Other calculus sites
Chapter 2: Integration methods
Written Notes
I 2-1:
Integration by substitution
I 2-2:
Integration by parts, the theory aspects
I 2-3:
Integration by parts with two visible factors
I 2-4:
Integration by parts with a single visible factor
I2-5:
Integration by parts with cycling steps
I 2-6:
Reduction formulae through integration by parts
I 2-7:
Trigonometric integrals by basic methods
I 2-8:
Trigonometric integrals by advanced methods
I 2-9:
Integration by inverse substitution by using the sine function
I 2-10:
Integration by inverse substitution by using the secant function
I 2-11:
Integration by inverse substitution by using the tangent function
I 2-12:
Integration by inverse substitution by using hyperbolic functions
I 2-13:
Partial fractions: preparation
I 2-14:
Partial fractions with non-repeated linear factors
I 2-15:
Partial fractions with non-repeated irreducible quadratic factors
I 2-16:
Partial fractions, the general case
Videos
Change of variable 1
Change of variable 2
Integration by parts 1
Integration by parts 2
Trig integrals
Inverse trig substitution 1
Inverse trig substitution 2
Inverse trig substitution 3
Partial fractions 1
Partial fractions 2
Partial fractions 3