Integrals

• Antiderivatives
• Riemann sum
• Definite integral
• Fundamental theorem of calculus

Integration Techniques

• U-Substitution
• Integration by parts
• Integration using trigonometric identities
• Trigonometric substitution
• Integration of rational functions by partial fractions
• Improper integrals
• Numerical integration

Integration Applications

• Areas between curves
• Volumes of solid with known cross-sections
• Volumes of solids of revolution – Disc method
• Volumes of solids of revolution – Shell method
• Average value of a function
• Arc length

Differential Equations

• Introduction to differential equations
• Separable equations
• Applications to differential equations
• Slope fields
• Euler’s method

Sequence and Series

• Introduction to sequences
• Monotonic and bounded sequences
• Introduction to infinite series
• Convergence and divergence of normal infinite series
• Convergence & divergence of geometric series
• Convergence & divergence of telescoping series
• Divergence of harmonic series
• P Series
• Alternating series test
• Divergence test
• Comparison & limit comparison test
• Integral test
• Ratio test
• Root test
• Absolute & conditional convergence
• Radius and interval of convergence with power series
• Functions expressed as power series
• Taylor series and Maclaurin series
• Approximating functions with Taylor polynomials and error bounds

Parametric Equations and Polar Coordinates

• Defining curves with parametric equations
•  Tangent and concavity of parametric equations
• Area of parametric equations
• Arc length and surface area of parametric equations
• Polar coordinates
• Tangents of polar curves
• Area of polar curves
• Arc length of polar curves

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