We at My Engineering Buddy offer Live Online Homework Help, Live Online Tutoring Sessions, Lab Reports, Projects and much more in following topics of calculus. Calculus is basically divided into calculus 1 and calculus 2. Calculus 3 is three dimensional calculus and also called Multivariable Calculus (we have not covered calculus 3 topics in this post).

## Calculus-1 topics

• Limits and continuity
• Estimating limits from tables
• Estimating limits from graphs
• Formal definition of limits (epsilon-delta)
• Properties of limits
• Limits using algebraic manipulation
• Limits by direct substitution
• Strategy in finding limits
• Squeeze theorem
• Continuity at a point
• Continuity over an interval
• Types of discontinuities
• Removing discontinuities
• Limits at infinity
• Infinite limits
• Intermediate value theorem
• Derivatives: definition and basic rules
• Average vs. instantaneous rate of change
• Secant lines
• Estimating derivatives
• Differentiability
• Power rule
• Combining the power rule with other derivative rules
• Derivatives of cos(x), sin(x), 𝑒ˣ, and ln(x)
• Product rule
• Quotient rule
• Derivatives: chain rule and other advanced topics
• Implicit differentiation
• Differentiating inverse functions
• Derivatives of inverse trigonometric functions
• Strategy in differentiating functions
• Differentiation using multiple rules
• Second derivatives
• Disguised derivatives
• Logarithmic differentiation
• Applications of derivatives
• Meaning of the derivative in context
• Straight-line motion
• Non-motion applications of derivatives
• Introduction to related rates
• Solving related rates problems
• Approximation with local linearity
• L’Hôpital’s rule
• L’Hôpital’s rule: composite exponential functions
• Analyzing functions
• Mean value theorem
• Extreme value theorem and critical points
• Relative (local) extrema
• Absolute (global) extrema
• Concavity and inflection points intro
• Analyzing concavity and inflection points
• Second derivative test
• Sketching curves
• Connecting f, f’, and f”
• Solving optimization problems
• Analyzing implicit relations
• Integrals
• Accumulations of change
• Approximation with Riemann sums
• Summation notation review
• Riemann sums in summation notation
• Defining integrals with Riemann sums
• Fundamental theorem of calculus and accumulation functions
• Interpreting the behavior of accumulation functions
• Properties of definite integrals
• Fundamental theorem of calculus and definite integrals
• Reverse power rules
• Indefinite integrals of common functions
• Definite integrals of common functions
• Integrating with u-substitution
• Integrating using long division and completing the square, Integrating using trigonometric identities
• Differential equations
• Verifying solutions for differential equations
• Sketching slope fields,
• Reasoning using slope fields
• Separation of variables
• Particular solutions to differential equations
• Exponential models
• Applications of integrals
• Average value of a function
• Straight-line motion
• Non-motion applications of integrals
• Area: vertical area between curves
• Area: horizontal area between curves
• Area: curves that intersect at more than two points
• Volume: triangles and semicircles cross-sections
• Volume: squares and rectangles cross-sections
• Volume: disc method (revolving around x- and y-axes)
• Volume: disc method (revolving around other axes)
• Volume: washer method (revolving around x- and y-axes)
• Volume: washer method (revolving around other axes)

## Calculus-2 Topics

• Integrals review
• Accumulations of change
• Approximation with Riemann sums
• Summation notation
• Riemann sums in summation notation
• Defining integrals with Riemann sums
• Fundamental theorem of calculus and accumulation functions
• Interpreting the behavior of accumulation functions
• Properties of definite integrals
• Fundamental theorem of calculus and definite integrals
• Reverse power rule
• Indefinite integrals of common functions
• Definite integrals of common functions
• Integration techniques
• Integrating with u-substitution
• Integrating using long division and completing the square
• Integrating using trigonometric identities
• Trigonometric substitution
• Integration by parts
• Integrating using linear partial fractions
• Improper integrals: Integration techniques
• Differential equations
• Verifying solutions for differential equations
• Sketching slope fields
• Reasoning using slope fields
• Approximation with Euler’s method
• Separation of variables
• Particular solutions to differential equations
• Exponential models
• Logistic models
• Applications of integrals
• Average value of a function
• Straight-line motion
• Non-motion applications of integrals
• Area: vertical area between curves
• Area: horizontal area between curves
• Area: curves that intersect at more than two points
• Volume: squares and rectangles cross-sections
• Volume: triangles and semicircles cross-sections
• Volume: disc method (revolving around x- and y-axes
• Volume: disc method (revolving around other axes)
• Volume: washer method (revolving around x- and y-axes)
• Volume: washer method (revolving around other axes)
• Arc length
• Parametric equations, polar coordinates, and vector-valued functions
• Parametric equations
• Second derivatives of parametric equations
• Arc length: parametric curves
• Vector-valued functions
• Planar motion
• Polar functions
• Area: polar regions (single curve)
• Area: polar regions (two curves)
• Arc length: polar curves
• Series
• Convergent and divergent infinite series
• Infinite geometric series
• nth-term test
• Integral test
• Harmonic series and p-series
• Comparison tests
• Alternating series test
• Ratio test
• Absolute and conditional convergence
• Alternating series error bound
• Taylor and Maclaurin polynomials
• error bound
• Power series
• Function as a geometric series
• Maclaurin series of eˣ, sin(x), and cos(x)
• Representing functions as power series

Check wikipedia page to see the complete list of topics in calculus 1,2 and more.