CALCULUS II

AIM

To teach fundamental math contents, methods and techniques, and its applications for the study of Engineering.

CONTENT

This course contains; Infinite Sequences: Limits of Sequences of Numbers, Subsequences, Monotonic Sequence Theorem,Infinite Sequences and Series: Series of Nonnegative Terms, Alternating Series, Absolute and Conditional Convergence,Power Series: Interval of Convergence, Radius of Convergence, Term by Term Differentiation, Term by Term Integration,Taylor Series,Parametric Equations and Polar Curves,Parametric Equations and Polar Curves,Vectors and Geometry of Space: Vectors in Space, Dot and Cross Products, Lines and Planes in Space, Cylinders and Quadric Surfaces ,Vectors and Geometry of Space: Vectors in Space, Dot and Cross Products, Lines and Planes in Space, Cylinders and Quadric Surfaces ,Functions of Several Variables: Limits and Continuity, Partial Derivatives, Directional Derivative,Functions of Several Variables: Limits and Continuity, Partial Derivatives, Directional Derivative,Extreme Values of Multivariable Functions, Lagrange Multiplier,Extreme Values of Multivariable Functions, Lagrange Multiplier,Multiple Integrals: Double Integrals, Areas, Double Integrals in Polar Form, Triple Integrals in Rectangular,Cylindirical and Spherical Coordinates,Multiple Integrals: Double Integrals, Areas, Double Integrals in Polar Form, Triple Integrals in Rectangular,Cylindirical and Spherical Coordinates.

1. 1

   1. Use the concept of polar coordinates to find areas, arc length of curves, and representations of conic sections.

   Taught by: Problem Solving Method, Self Study Method, Lecture Method · Assessed by: Traditional Written Exam, Homework

2. 2

   2. Apply dot or cross product to calculate angles between vectors, orientation of axes, areas of triangles and parallelograms in space, scalar and vector projections, volumes of parallelepipeds and distance between a point and a plane in the space.

   Taught by: Problem Solving Method, Self Study Method, Lecture Method · Assessed by: Traditional Written Exam, Homework

3. 3

   3. Recognize multivariable functions to compute limits, partial derivatives and directional derivatives, extreme values, tangent planes graphically, numerically and algebraically.

   Taught by: Problem Solving Method, Self Study Method, Lecture Method · Assessed by: Traditional Written Exam, Homework

4. 4

   4. Use multiple integrals to compute areas and volumes.

   Taught by: Problem Solving Method, Self Study Method, Lecture Method · Assessed by: Traditional Written Exam, Homework

5. 5

   5. Determine convergence or divergence of sequences and series.

   Taught by: Problem Solving Method, Self Study Method, Lecture Method · Assessed by: Traditional Written Exam, Homework

6. 6

   6. Find Power and Taylor Series of a function.

   Taught by: Problem Solving Method, Self Study Method, Lecture Method · Assessed by: Traditional Written Exam, Homework

WEEKLY PLAN

1. WEEK 1

   Infinite Sequences: Limits of Sequences of Numbers, Subsequences, Monotonic Sequence Theorem

   Preparation: Functions, Limit

2. WEEK 2

   Infinite Sequences and Series: Series of Nonnegative Terms, Alternating Series, Absolute and Conditional Convergence

3. WEEK 3

   Power Series: Interval of Convergence, Radius of Convergence, Term by Term Differentiation, Term by Term Integration

   Preparation: Absolute Value, Integral, Derivative

4. WEEK 4

   Taylor Series

5. WEEK 5

   Parametric Equations and Polar Curves

   Preparation: Polynomial functions, Power functions, Trigonometric functions, Derivative of a function, Chain rule.

6. WEEK 6

   Parametric Equations and Polar Curves

   Preparation: Polynomial functions, Power functions, Trigonometric functions, Derivative of a function, Chain Rule.

7. WEEK 7

   Vectors and Geometry of Space: Vectors in Space, Dot and Cross Products, Lines and Planes in Space, Cylinders and Quadric Surfaces

   Preparation: Equations of lines and circles, Real space

8. WEEK 8

   Vectors and Geometry of Space: Vectors in Space, Dot and Cross Products, Lines and Planes in Space, Cylinders and Quadric Surfaces

   Preparation: Equations of lines and circles, Real space.

9. WEEK 9

   Functions of Several Variables: Limits and Continuity, Partial Derivatives, Directional Derivative

   Preparation: Single Variable Functions, Limit and Continuity, Derivative

10. WEEK 10

    Functions of Several Variables: Limits and Continuity, Partial Derivatives, Directional Derivative

    Preparation: Single Variable Functions, Limit and Continuity, Derivative

11. WEEK 11

    Extreme Values of Multivariable Functions, Lagrange Multiplier

    Preparation: Derivative, Extreme Values of Single Variable Functions

12. WEEK 12

    Extreme Values of Multivariable Functions, Lagrange Multiplier

    Preparation: Derivative, Extreme Values of Single Variable Functions

13. WEEK 13

    Multiple Integrals: Double Integrals, Areas, Double Integrals in Polar Form, Triple Integrals in Rectangular,Cylindirical and Spherical Coordinates

    Preparation: Definite Integrals, Polar Coordinates

14. WEEK 14

    Multiple Integrals: Double Integrals, Areas, Double Integrals in Polar Form, Triple Integrals in Rectangular,Cylindirical and Spherical Coordinates

    Preparation: Definite Integrals, Polar Coordinates

ASSESSMENT

• Rate of Midterm Exam to Success30%
• Rate of Final Exam to Success70%

WORKLOAD

READING

• Thomas’ Calculus, 12th ed., G. B. Thomas, Jr. and M. D. Weir and J. Hass, Addison-Wesley

TEACHING STAFF

• Assist.Prof. Özge BİÇER ÖDEMİŞCOORDINATOR
• Assist.Prof. Özge BİÇER ÖDEMİŞ