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.
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I have an M.Tech. in Mathematics and Computing from IIT Guwahati, and I am currently doing my PhD at the same institution. I love teaching mathematics (especially higher mathematics).I like it a lot, and I keep sharing my mathematics experience by writing informative blog articles.
I worked on Chegg as a subject matter expert in mathematics and solved more than 5000 problems before joining MEB. I have mastery over calculus 1, calculus 2, calculus 3, vector calculus, fractional calculus, calculus of variations, finite element methods, linear algebra (advanced), ordinary and partial differential equations, numerical methods, discrete mathematics, probability and statistics, laplace transformation, mathematical models, and special functions like beta function, gamma function, legendre polynomial, hermite polynomial, bessel functions, etc.
