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)

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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.

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