Sequences and series. Power series. Taylor polynomials, Taylor series and approximation. Visualizing functions of several variables; graphs and contour diagrams. Vectors. Differentation in several variables; partial and directional derivatives. Linear and quadratic approxiamtion. Classification of local extrema. Optimization, Lagrange Multipliers. Integration in several variables. Iterated integrals. Change of variables; polar, cylindrical and spherical coordinates.

### Calculus II (MATH 102)

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Programs\Type | Required | Core Elective | Area Elective |

BA- Political Science | |||

BA-Cultural Studies | |||

BA-Cultural Studies | |||

BA-Economics | |||

BA-Economics | |||

BA-International Studies | |||

BA-International Studies | |||

BA-Management | |||

BA-Management | |||

BA-Political Sci.&Inter.Relat. | |||

BA-Political Sci.&Inter.Relat. | |||

BA-Psychology | |||

BA-Psychology | |||

BA-Social & Political Sciences | |||

BA-Visual Arts&Visual Com.Des. | |||

BA-Visual Arts&Visual Com.Des. | |||

BS-Biological Sci.&Bioeng. | |||

BS-Computer Science & Eng. | |||

BS-Computer Science & Eng. | |||

BS-Electronics Engineering | |||

BS-Electronics Engineering | |||

BS-Industrial Engineering | |||

BS-Manufacturing Systems Eng. | |||

BS-Materials Sci. & Nano Eng. | |||

BS-Materials Science & Eng. | |||

BS-Mechatronics | |||

BS-Mechatronics | |||

BS-Microelectronics | |||

BS-Molecular Bio.Gen.&Bioeng | |||

BS-Telecommunications |

### CONTENT

### OBJECTIVE

To introduce series and concepts of multivariable calculus, to relate notions in multivariable calculus to their analogues in single variable.

### LEARNING OUTCOME

Understand the idea of integration over unbounded intervals and compute them

Define the notion of convergence of series and use various tests to determine series convergence

Find Taylor representations of functions and approximate functions via Taylor polynomials

Understand and use the concept of a function of several variables, draw graphs in 3-space

Use the properties of vectors and operations with vectors

Compute partial derivatives, directional derivatives and write equations of tangent planes to surfaces

Apply partial derivatives to find and test local extrema.

Evaluate double integrals in Cartesian and polar coordinates and triple integrals in Cartesian coordinates

### Update Date:

### ASSESSMENT METHODS and CRITERIA

Percentage (%) | |

Final | 25 |

Midterm | 50 |

Exam | 20 |

Participation | 5 |

### RECOMENDED or REQUIRED READINGS

Textbook |
Calculus Early Transcendentals 2nd Edition (Global Edition), Briggs, Cochran & Gillett. |