Higher mathematics consists of a large number of sections, and gaps in any of them cause problems in the rest. That is why there is no time to “bounce around”, you should immediately get involved in the work and close the emerging issues.
Course syllabus:
Mathematical Analysis I (Limits)
Lesson 1: Sequences
Lesson 2: Limits of a sequence
Lesson 3: Functions and their properties
Lesson 4. Limits of a function
Lesson 5. The first remarkable limit
Lesson 6. The second remarkable limit
Lesson 7 Continuity and points of discontinuity of a function
Term paper
Mathematical analysis II (Derivative)
Lesson 1 The derivative. Definition. Rules for calculating derivatives. Table of derivatives of elementary functions.
Lesson 2. The derivative of a compound function.
Lesson 3. The derivative of a function defined parametrically.
Lesson 4 The derivative of an implicit function
Lesson 5. Derivatives of higher orders
Lesson 6. The differential
Lesson 7: Tangent and normal
Lesson 8. Lopital’s rule
Lesson 9. Taylor’s formula
Term paper
Mathematical analysis III (graphing)
Lesson 1: General scheme of investigation of a function. Ascending/descending functions. Extremes. Convexity/curvature/ inflection points. Asymptotes
Lesson 2: Power functions and polynomials
Lesson 3. Fractional-rational functions
Lesson 4: Irrational functions
Lesson 5 Trigonometric functions
Lesson 6. Calculus functions
Lesson 7 Logarithmic functions
Term paper
Mathematical analysis IV (An undefined integral)
Lesson 1 Tabular integration
Lesson 2: Integration by substitution
Lesson 3: Integration by parts
Lesson 4 Integral with a quadratic trinomial
Lesson 5: Integrating rational functions
Lesson 6 Integration of irrational functions
Lesson 7. Integrating trigonometric functions.
Lesson 8. Mixed examples of integration
Term paper
Mathematical analysis V (Series)
Series, definition, sum of series. The necessary sign of convergence.
Series with positive terms (comparison signs, Dalembert, Cauchy, integral)
Series with alternating terms
Approximate computation of series sums
Functional series, the area of convergence
Power series
Taylor series
Fourier series