Calculus I & II summary notes under MATH-M 211 & 212 from the Indiana University Bloomington. 2022 written, 50 page notes cover 11 sub topics.

• Class Year
• 2022
• A
• Number of Pages
• 50
• Staff Rating
• 4.75/5

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Calculus I & II (MATH-M 211) summary notes covering following topics:

1. Review: Functions
• Functions and their graphs
• Transformations and combinations of graphs
• Trigonometric functions
2. Limits and continuity
• Limit of a function and limit laws
• Precise definition of a limit
• One-sided limits
• Continuity
• Limits involving infinity and asymptotes
3. Differentiation
• Tangent lines and the derivative at a point
• The derivative as a function
• Differentiation rules
• The derivative as a rate of change
• Derivatives of trigonometric functions
• The chain rule
• Implicit differentiation
• Related rates
• Linearization and differentials
4. Applications of differentiation
• Extreme values of functions on closed interval
• The mean value theorem
• Monotonic functions and the first derivative test
• Concavity and curve sketching
• Applied optimization
• Newton’s method
• Antiderivatives
5. Integration
• Areas and estimating with finite sums
• Sigma notation and limits of finite sums
• Definite integrals
• The fundamental theorem of calculus
• Indefinite integrals and the substitution method
• Definite integral substitutions and the area between curves
6. Applications of definite integration
• Volumes using disks and washers
• Volumes using shells
• Arc length
• Areas of surfaces of revolution
• Work and fluid forces
• Moments and centers of mass
7. Transcendental functions
• Inverse functions and their derivatives
• Natural logarithms
• Exponential functions
• Exponential change and separable differential equations
• Indeterminate forms and L’Hˆopital’s rule
• Inverse trigonometric functions
• Hyperbolic functions
• Relative rates of growth
8. Techniques of integration
• Using basic integration formulae
• Integration by parts
• Trigonometric integrals
• Trigonometric substitutions
• Integration of rational functions by partial functions
• Integral tables and computer algebra systems
• Numerical integration
• Improper integrals
• Probability
9. First-order differential equations
• Solutions, slope fields and Euler’s method
• First-order linear equations
• Applications
• Graphical solutions of autonomous equations
• Systems of equations and phase planes
10. Infinite sequences and series
• Sequences
• Infinite series
• The integral test
• Comparison tests
• Absolute convergence, ratio and root tests
• Alternating series and conditional convergence
• Power series
• Taylor and Maclaurin series
• Convergence of Taylor series
• Applications of Taylor series
11. Parametric equations and polar coordinates
• Parametrizations of plane curves
• Calculus with parametric curves
• Polar coordinates
• Graphing polar coordinate equations
• Areas and lengths in polar coordinates
• Conic sections
• Conics in polar coordinates