Calculus II for IT
Calculus II for IT
These class notes must be studied together with the ppt slides we discuss in class. Those written comments are just complementary notes that aim to get the students' attention to certain stuff that I, as an instructor, see important.
Chapter 7: Techniques of Integration
Chapter 10: Parametric equations and polar coordinates
Chapter 11: Sequences and Series
Integral test (Not included in this course) But the p-series is included
Comparison test(Not included in this course)
Chapter 14: Functions of several variables
Required or Elective: Obligatory for all IT Students.
Course Prerequisites: N/A.
Catalog Description:
Hyperbolic Functions, Integration of Transcendental Functions, Techniques of Integration: Integration by Substitution (Review), Integration by Parts, Integration Including Powers of Trigonometric Functions, Integration by Trigonometric Substitution, Partial Fractions, Improper Integrals, Sequences, Limit of Sequence; Series: Convergent and Divergent Series; Series Tests for Convergence: Partial Sums, Telescoping Series, Geometric Series, Base Divergence Test, P-series Test, Ratio Test, Root Test, Absolute Convergence Test, Alternating Series Test, Conditional Convergence; Power Series and Taylor series, Interval and Radius of Convergence, Parametric Equations of Curves in Plane, Polar Coordinates, Graphs in Polar Coordinates, Functions of Several Variables: Partial Derivatives, Second Order Pratial Derivative Test, Double Integrals: Double Integrals on Rectangular Region, Double Integral on General Region, Double Integrals in polar Coordinates.
Text Book and Related Course Materials:
Textbook : Stewart’ Calculus, 9th edition, Stewart, Clegg, and Watson.
Online homework's and their solutions.
Previous exams.
Course Objectives and Relation to The Program Educational Objectives:
Students shall demonstrate the ability to:
Calculate integrations using different techniques.
Test if an infinite sequence converges or diverges.
Test if an infinite series converges or diverges.
Identify power series and construct the interval and radius of convergence.
Identify Taylor series and apply them to solve different problems.
Describe the curves in two dimensions using parametric equations and apply the parametric equations to inspect the properties of curves.
Describe the polar coordinates, illustrate their relationship to xy-coordinates, and use them in different applications.
Contribution to The Professional Component: Mathematics and Basic Sciences(100%).
Expected Level of Proficiency for Students Entering The Course: Mathematics (High).
Will this course involve computer assignments? Yes.
Will this course have TA(s) when offered? No.
Level of contribution to program outcomes:
Strong: a,e
Average: k
Weak: i
Upon completion of this course, students will have had an opportunity to learn about the following:
An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics
ABET’s course outcomes (a-k) criteria
Engineering programs must demonstrate that their graduates have:
1. An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics.
2. An ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors.
3. An ability to communicate effectively with a range of audiences.
4. An ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts.
5. An ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives.
6. An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions.
7. An ability to acquire and apply new knowledge as needed, using appropriate learning strategies.
Required or Elective: Obligatory for all IT Students.
Course Prerequisites: N/A.
Catalog Description:
Hyperbolic Functions, Integration of Transcendental Functions, Techniques of Integration: Integration by Substitution (Review), Integration by Parts, Integration Including Powers of Trigonometric Functions, Integration by Trigonometric Substitution, Partial Fractions, Improper Integrals, Sequences, Limit of Sequence; Series: Convergent and Divergent Series; Series Tests for Convergence: Partial Sums, Telescoping Series, Geometric Series, Base Divergence Test, P-series Test, Ratio Test, Root Test, Absolute Convergence Test, Alternating Series Test, Conditional Convergence; Power Series and Taylor series, Interval and Radius of Convergence, Parametric Equations of Curves in Plane, Polar Coordinates, Graphs in Polar Coordinates, Functions of Several Variables: Partial Derivatives, Second Order Pratial Derivative Test, Double Integrals: Double Integrals on Rectangular Region, Double Integral on General Region, Double Integrals in polar Coordinates.
Text Book and Related Course Materials:
Textbook : Stewart’ Calculus, 9th edition, Stewart, Clegg, and Watson.
Online homework's and their solutions.
Previous exams.
Course Objectives and Relation to The Program Educational Objectives:
Students shall demonstrate the ability to:
Calculate integrations using different techniques.
Test if an infinite sequence converges or diverges.
Test if an infinite series converges or diverges.
Identify power series and construct the interval and radius of convergence.
Identify Taylor series and apply them to solve different problems.
Describe the curves in two dimensions using parametric equations and apply the parametric equations to inspect the properties of curves.
Describe the polar coordinates, illustrate their relationship to xy-coordinates, and use them in different applications.
Contribution to The Professional Component: Mathematics and Basic Sciences(100%).
Expected Level of Proficiency for Students Entering The Course: Mathematics (High).
Will this course involve computer assignments? Yes.
Will this course have TA(s) when offered? No.
Level of contribution to program outcomes:
Strong: a,e
Average: k
Weak: i
Upon completion of this course, students will have had an opportunity to learn about the following:
An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics
ABET’s course outcomes (a-k) criteria
Engineering programs must demonstrate that their graduates have:
1. An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics.
2. An ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors.
3. An ability to communicate effectively with a range of audiences.
4. An ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts.
5. An ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives.
6. An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions.
7. An ability to acquire and apply new knowledge as needed, using appropriate learning strategies.