Syllabus Number 8
Course
Name
CalculusⅠ
Semester, Year
First Semester, 2017
Course level
1000
Instructor(s)
(Institution)
YORDANOV, Borislav (国際連携機構)
Course
Objectives
Course Goals
Number of Credits
2 credits
Course Number
027009
This course covers limits and derivatives of functions in one and several variables.
Students should master the basics of
(1) limits of sequences and functions based on intuitive definition of limit;
(2) differentiation of functions in one variable;
(3) differentiation of functions in several variables.
Course
Schedule
Week 1 Sequences - definition of a sequence, limit of a sequence
Week 2 Functions ? functions, graph of a function, types of functions, transcendental functions
Week 3 Functions ? limit of a function, continuity and intermediate value theorem, inverse functions
Week 4 Differentiation (one variable) ? definition, tangent line, differentiation of composite and inverse functions
Week 5 Differentiation (one variable) ? rules for differentiation, derivatives of elementary functions
Week 6 Differentiation (one variable) ? mean value theorem, l'Hopital rule
Week 7 Differentiation (one variable) ? Taylor expansion, asymptotic expansions
Week 8 Extreme value problems (one variable) ? graphs, min/max values
Week 9 Extreme value problems (one variable) ? applications
Week 10 Differentiation (two variables) ? functions of two and more variables, partial derivatives, differentials
Week 11 Differentiation (two variables) ? implicit functions, Jacobian, partial derivatives using the Jacobian: implicit function
theorem
Week 12 Differentiation (two variables) ?Taylor expansion, directional derivatives
Week 13 Differentiation (two variables) ? applications of partial derivatives: tangent plane to a surface
Week 14 Extreme problem (two variables) ? Hesse matrix, min/max values, saddle points
Week 15 Extreme problem (two variables) ? Lagrange method for optimization under constraints
Week 16 Final exam
Homework
Students are required to submit one set of homework problems per week. In addition,
students are expected to study for a couple of hours before or after each lecture.
Grading
System
Grades are based on class participation and quizzes (40%), homework assignments (30%)
and final exam (30%). The following grading scale will be applied: 0%-59% = F,
60%-69% = D to C-, 70%-79% = C to C+, 80%-89% = B to B+, 90%-100% = A- to A.
Textbooks /
Reading List
The textbook and other reading materials will be provided by the teacher.
Websites
Website of
Laboratory
Additional
Information
For further details, please visit instructor’s home page:
http://www.math.sci.hokudai.ac.jp/~yordanov/<http://www.math.sci.hokudai.ac.jp/%7Ekubo