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Calculus I

• Course name: Calculus I
• Course number: XYZ

Course Characteristics

Key concepts of the class

• Calculus for the functions of one variable: differentiation
• Calculus for the functions of one variable: integration
• Basics of series
• Multivariate calculus: derivatives, differentials, maxima and minima
• Multivariate integration
• Functional series. Fourier series
• Integrals with parameters

What is the purpose of this course?

The course is designed to provide Software Engineers the knowledge of basic (core) concepts, definitions, theoretical results and techniques of calculus for the functions of one and several variables. The goal of the course is to study basic mathematical concepts that will be required in further studies.

This calculus course will provide an opportunity for participants to understand key principles involved in differentiation and integration of functions: solve problems that connect small-scale (differential) quantities to large-scale (integrated) quantities,
get hands-on experience with the integral and derivative applications and of the inverse relationship between integration and differentiation.

All definitions and theorem statements (that will be given in lectures and that are needed to explain the keywords listed above) will be formal, but just few of these theorems will be proven formally. Instead (in the tutorial and practice classes) we will try these definitions and theorems on work with routine exercises and applied problems.

Course objectives based on Bloom’s taxonomy

- What should a student remember at the end of the course?

By the end of the course, the students should be able to

• what the partial and directional derivatives of functions of several variables are
• basic techniques of integration of functions of one variables
• how to calculate line and path integrals
• distinguish between point wise and uniform convergence of series and improper integrals
• decompose a function into Fourier series
• calculate Fourier transform of a function

- What should a student be able to understand at the end of the course?

By the end of the course, the students should be able to

• how to find minima and maxima of a function of various orders
• how to represent double integrals as iterated integrals and vice versa
• what the length of a curve and the area of a surface is
• properties of uniformly convergent series and improper integrals
• how to find Fourier transform of a function

- What should a student be able to apply at the end of the course?

By the end of the course, the students should be able to

• take derivatives of various type functions and of various orders
• integrate the functions of one and several variables
• apply definite integration
• expand functions into Taylor series
• find multiple, path, surface integrals
• find the range of a function in a given domain
• decompose a function into Fourier series

Course evaluation

Course grade breakdown

Type	Points
Labs/seminar classes	12
Interim performance assessment	48
Exams	140

Grades range

Course grading range

Grade	Points
A	[180, 200]
B	[150, 179]
C	[120, 149]
D	[0, 119]