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).
Calculus1 topics
 Limits and continuity
 Estimating limits from tables
 Estimating limits from graphs
 Formal definition of limits (epsilondelta)
 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
 Straightline motion
 Nonmotion 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 usubstitution
 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
 Straightline motion
 Nonmotion 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 crosssections
 Volume: squares and rectangles crosssections
 Volume: disc method (revolving around x and yaxes)
 Volume: disc method (revolving around other axes)
 Volume: washer method (revolving around x and yaxes)
 Volume: washer method (revolving around other axes)
Calculus2 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 usubstitution
 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
 Straightline motion
 Nonmotion 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 crosssections
 Volume: triangles and semicircles crosssections
 Volume: disc method (revolving around x and yaxes
 Volume: disc method (revolving around other axes)
 Volume: washer method (revolving around x and yaxes)
 Volume: washer method (revolving around other axes)
 Arc length
 Parametric equations, polar coordinates, and vectorvalued functions
 Parametric equations
 Second derivatives of parametric equations
 Arc length: parametric curves
 Vectorvalued 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
 nthterm test
 Integral test
 Harmonic series and pseries
 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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