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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