====== FSc Part 2 (KPK Boards) ====== {{ :fsc:fsc-part-2-kptb.jpg?nolink |A Textbook of Mathematics For Class XII}} Notes of FSc Part 2 of "A Textbook of Mathematics For Class XII" published by Khyber Pakhtunkhwa Textbook Board, Peshawar. We are posting the notes chapter-wise. These notes are shared as open educational resources. This page will be continuously updated. ^ Author: | Muhammad Ashfaq | ^ Type: | Solutions only | ^ Sender: | Muhammad Marwan | ^ Format: | PDF Scanned (Handwritten) | ===== Unit 01: Functions and Limits ===== {{ :fsc:kpk_fsc_part_2:kpk-unit1-fsc2.jpg?nolink |Horizontal asymptote to the curve}} === Objectives === After reading this unit the students will be able to: * identify the domain and range of a functions through graphs. * draw the graph of modulus function and identify its domain and range. * recognize the composition of a function and then to find out the composition of two functions. * describe the inverse of a function and then to find out the inverse of composition of two functions. * recognize the algebraic and transcendental functions as well as the concepts of explicit, implicit and parametric functions. * display graphically the explicit, implicit and parametric functions as well as the compound functions. * introduce the limit of a function with respect to real number intervals on the real number line, the open and closed intervals and its location on a real number line. * explain the meaning of x tends to zero, x tends to a and x tends to infinity * define the limit of a sequence when the limit of a sequence with nth term is given. * define the limit of a function and the statement of theorems on limits of sum, difference, product and quotient of functions. * evaluate the limits of a function in case of some special functions. * evaluate the limit of algebraic, exponential and trigonometric functions. * introduce the continuous and discontinuous functions. * recognize the left hand and right hand limits through examples. * define the continuity of a function at a point and in an interval. * test the continuity and discontinuity of a function a point and in an interval. ==== Download ==== {{:fsc:kpk_fsc_part_2:ch01-function-and-limits-fsc2-kpk.pdf|}} %%|%% ===== Unit 02: Differentiation ===== === Objectives === After reading this unit the students will be able to: * distinguish between independent and dependent variables. * estimate the change in the dependent variable, when the independent variable is incremented or decremented. * explain the concepts of a rate of change. * define the derivative of a function as an instantaneous rate of change of variable with respect to another variable. * define derivative or differential coefficient of a function. * differentiate $y=x^n$ and $y=(ax+b)^n$ by first principle rule. * introduce the theorems of differentiation, such as the derivative of a constant function, the derivative of any constant multiple of a function, the derivative of a sum or difference of two functions, the derivative of the product of two functions and the derivative of a quotient of two functions. * apply theorems of differentiation in solving problems. * introduce chain rule of differentiation in different situations. * introduce implicit differentiation of a function. * introduce differentiation of trigonometric and inverse trigonometric functions. * introduce differentiation of exponential and logarithmic functions. * introduce the differentiation of hyperbolic and inverse hyperbolic functions. ==== Download ==== {{:fsc:kpk_fsc_part_2:ch02-differentiation-fsc2-kpk.pdf|}} %%|%% ===== Unit 03: Higher Order Derivative and Application ===== {{ :fsc:kpk_fsc_part_2:kpk-unit3-fsc2.jpg?nolink |Geometrical Interpretation of Derivative}} === Objectives === After reading this unit the students will be able to: * Integration ==== Download ==== {{ :fsc:kpk_fsc_part_2:ch03-higher-oreder-derivative-and-application-fsc2-kpk.pdf |}} %%|%% ===== Unit 04: Differentiation of Vector Functions ===== === Objectives === After reading this unit the students will be able to: * Differentiation ==== Download ==== {{:fsc:kpk_fsc_part_2:ch04-differentiation-of-vector-functions-fsc2-kpk.pdf|}} %%|%% View Online ===== Unit 05: Integration ===== === Objectives === After reading this unit the students will be able to: * Integration ==== Download ==== {{:fsc:kpk_fsc_part_2:ch05-integration-fsc2-kpk.pdf|}} %%|%% View Online ===== Unit 09: Integration ===== === Objectives === This unit tells us, how to: * define the differential equation, its order, degree, general and particular solutions, and its identification as linear and nonlinear ordinary differential equations. * demonstrate the concept in forming a differential equation. * solve the first order linear and nonlinear ordinary differential equations by separable variable form, and homogenuous form and then how to reduce differential equations in standard form of homogenuous. * solve the real life problems related to differential equations. * define the orthogonal trajectories and then how to show the orthogonal trajectories of the two families of curve. ==== Download ==== {{ :fsc:kpk_fsc_part_2:ch09-differential-equations-fsc2-kpk.pdf |}} %%|%% View Online {{tag> FSc KPK_FSc_Part2}}