GATE Data Science and AI Calculus and Optimization Syllabus

Functions of a single variable, limit, continuity and differentiability, Taylor series, maxima and minima, optimization involving a single variable.

Here’s an overview of GATE Data Science and AI Calculus and Optimization Syllabus

1. Function: A function is a relation between a set of inputs (domain) and a set of possible outputs (codomain), where each input is related to exactly one output. It’s often denoted by ( f(x) ), where ( x ) is the input variable.
2. Limit: The limit of a function represents the behavior of the function as the input approaches a certain value. It’s denoted as ( \lim_{x \to a} f(x) ) and represents the value that ( f(x) ) approaches as ( x ) approaches ( a ).
3. Continuity and Differentiability:
   • Continuity refers to the property of a function where there are no abrupt jumps or breaks in the graph. A function is continuous at a point ( a ) if the limit of the function exists at ( a ) and is equal to the value of the function at ( a ).
   • Differentiability refers to the property of a function where it has a well-defined derivative at each point in its domain.
4. Taylor Series: A Taylor series is an infinite series representation of a function as an infinite sum of terms calculated from the values of its derivatives at a single point. It’s useful for approximating functions, especially around a specific point.
5. Maxima and Minima: Maxima and minima are points where a function reaches its highest or lowest value, respectively. They can occur at critical points where the derivative is zero or undefined, and at endpoints of intervals.
6. Optimization Involving a Single Variable: Optimization involves finding the maximum or minimum value of a function within a given domain. This can be achieved by identifying critical points, checking endpoints, and using the first or second derivative test to determine whether a critical point corresponds to a maximum, minimum, or neither.

Understanding these concepts is crucial for analyzing and manipulating functions of a single variable, which are foundational in calculus and mathematical modeling across various disciplines.

GATE DATA SCIENCE AND AI CALCULUS AND OPTIMIZATION FULL COURSE–Just at Rs.300

GATE DA Subject wise syllabus:

1. GATE DA Linear Algebra Syllabus
2. GATE DA Calculus and Optimization Syllabus
3. GATE DA Probability and Statistics Syllabus
4. GATE DA Python Programming Data Structures and Algorithms Syllabus
5. GATE DA DBMS and Warehousing Syllabus
6. GATE DA Machine Learning
7. GATE DA  Artificial Intelligence Syllabus