After completing this course, students should have developed a clear understanding of the fundamental concepts of single variable calculus and a range of skills allowing them to work effectively with the concepts.
The basic concepts are:
1. Derivatives as rates of change, computed as a limit of ratios
2. Integrals as a "sum," computed as a limit of Riemann sums
After completing this course, students should demonstrate competency in the following skills:
Use both the limit definition and rules of differentiation to differentiate functions.
Sketch the graph of a function using asymptotes, critical points, the derivative test for increasing/decreasing functions, and concavity.
Apply differentiation to solve applied max/min problems.
Apply differentiation to solve related rates problems.
Evaluate integrals both by using Riemann sums and by using the Fundamental Theorem of Calculus.
Apply integration to compute arc lengths, volumes of revolution and surface areas of revolution.
Evaluate integrals using advanced techniques of integration, such as inverse substitution, partial fractions and integration by parts.
Use L'Hospital's rule to evaluate certain indefinite forms.
Determine convergence/divergence of improper integrals and evaluate convergent improper integrals.
Determine the convergence/divergence of an infinite series and find the Taylor series expansion of a function near a point. Fourier series
Course Content (Syllabus)
Introduction to Trigonometry. Calculus of functions with one variable. Implicit differentiation. Inverse functions, inverse trigonometric functions and hyperbolic functions. The definition of indefinite integral and properties of indefinite integrals. Integration techniques. Application of integrals. Improper integrals. Parametric equations and polar coordinates. Sequences and Power Series. Taylor Series and Fourier Series. Applications
functions, limits, derivatives, integration, power series
Course Bibliography (Eudoxus)
Βιβλίο : ΛΟΓΙΣΜΟΣ ΜΙΑΣ ΜΕΤΑΒΛΗΤΗΣ (Θεωρία-Εφαρμογές σε Maple)., Βασίλειος Ρόθος και Χρυσοβαλάντης Σφυράκης
Βιβλίο : ΑΠΕΙΡΟΣΤΙΚΟΣ ΛΟΓΙΣΜΟΣ ΤΟΜΟΣ Ι, FINNEY R.L., WEIR M.D., GIORDANO F.R