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
Learning support resources
Learning skills
Pre-Engineering math
Other calculus sites
Chapter 5:
Basic applications of integration
Written Notes
I 5-1:
The four step process for building integrals
I 5-2:
Areas between two curves
I 5-3:
Arc length
I 5-4:
Surfaces of areas of revolution
I 5-5:
Volumes by slicing
I 5-6:
Volumes by disks and washers
I 5-7:
Volumes by shells
I 5-8:
Picking the right method to compute volumes
I 5-9:
Geometric quantities for parametric curves
I 5-10:
Geometric quantities for polar curves
I 5-11:
Work problems
I 5-12:
Fluid force problems
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