Course name: Calculus
COURSE CONTENT
The real line and coordinate plane. Functions and their graphs. Equations and inequations.
The problem of tangents. The derivative. Rates of change. Limits.
Derivatives, the product and quotient rules, composite functions and the chain rule, implicit functions.
Monotone functions. Maxima and minima. Convexity and points of inflection. Applied maximum and minimum problems.
Differentials and tangent line approximations. Indefinite integrals, integration by substitution and by parts. Mixed strategies. Differential equations. Separation of variables.
Definite integrals. The computation of areas. The fundamental theorem of calculus. Volumes: the disk and the shell methods.
Exponents and logarithms. The natural logarithm. Linear differential equations with applications.
The inverse trigonometric functions.
Integration by substitution. The partial fractions.
Indeterminate forms. Improper integrals. The normal distribution.
Sequences and series. Convergence tests. Absolute convergence. The interval of convergence. Differentiation and integration of power series. Taylor series and formula.
LEARNING OUTCOME
Perform routine algebraic manipulations. Solve simple equations and inequations, including simultaneous. Understand the basis of differential calculus, be able to differentiate and integrate functions, find maxima and minima and solve simple differential equations. Perform routine geometric and trigonometric manipulations.
CREDITS: 8
CONTACT INFORMATION
Prof. Pierantonio Legovini
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