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1.1.1 TA5101 APPLIED MATHEMATICS

Course code

TA5101

Number of

credits: 3

Semester:

I

Field of competence:

General

Remark:

Course type Class interaction

Course group Basic engineering science

Course title Geomathematics

Short description Basics of vector and matrix, scalar and vector field, scalar and vector

function, tensor and concet of anisotro! in geocience, modeling

su"surface geometr!, area and volume and and its alication in

geoscience, vector calculus #gradient, divergence, curl etc$ in

geoscience% &odeling "! deterministic theor! using diffrerential

e'uation and its alication for transort hanomena and evaluation of

natural resources% Basics in non(deterministic modeling in geoscience

#"asics in geostatistics$%

Goal After comletion of this course students )ere exected to "e a"le to

understand and al! modeling of transort henomenaand natural

resources evaluation%

Offered to *et% of &ining +ngineering acult!: TT& ITB

Related courses 1% Basics of Calculus -rere'uisites

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&etailed Course Content

'eek (opic Subtopic Actiity

1 30(0? Introduction2chedule, lecture aroach, s!lla"us, hand"oo, evaluation#mid, final$, exercise and grou roect, 'ui9, home )or,

note"oo = student it and mathe in geo(engineering in all%

4ecture,

discussion

6 03%0;

8ui9 1

Basics of vector and its alication

in geo(engineering

-oint, line, lain surface e'uation, normal vector, angle

"et)een surface, direction cosine, triangulation, area )ithin

triangle, geometric interretation of vector oeration%

4ecture,discussion

3 10%0;

8ui9 6

Basics of matrix and its alicationin geo(engineering

4inear s!stem of e'uation #determinant, coefficient and

augmented matrix$, &arov rocess #stochastic matrix,

transition matrix$, linear transformation #transformation

matrix or matrix of eigenvector$, rincial comonent

anal!sis #tensor, determinant$, tensor, eigenvalue =eigenvector, rincial direction, rincial comonent,

diagonali9ation, transformation from rincile axes,anistro! in geo(engineering #elastic deformation, flo),

assa! anisotro!, stresses in roc mass$%

4ecture,discussion

1@%0;8ui9 3Basics of vector differential calculus

ield, function, vector derivation and related theorems,variation, relative and a"solut variation, gradient, directionalderivative, divergence, curl etc%

4ecture,discussion

-roect 1

>ector, matrix, tensor and

anisotro!

An exeriment )ith assa! anisotro! and mineralisationGrou

roect

5 6%0;

8ui9

Alication of vector differential

calculus

Basics of continuum mechanics, "asics of transort

hanomena, e'uation of motion and e'uation of mass

"alance%

4ecture,

discussion

01%108ui9 5Basic of vector integral calculus

4ine, lain integral and surface integral%4ecture,

discussion

06%10

#$

-roect 6

Alication of ordinar! dou"le

scalar integral and "asic transorthanomen%

+valuation of andesitic roc resources and estimation of G

inflo) in a 'uar! of andesitic roc mining%

Grou

roect

@ 0?%10Alication of vector integral

calculus+stimation of coal and mineral resources%

4ecture,

discussion

0;%10#$

-roect 3Alication of vector integral calc%

+stimation of resource and G inflo) into mining front ofvein(t!ed gold deosit mining%

Grouroect

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'eek (opic Subtopic Actiity1%10

#(4+$>ector calculus and its alication *iscusiion and exercise "efore mid exam% *iscussion

?66%10

#$Class discussion *iscussion "efore mid evaluation% *iscussion

;

63%10

#$ Class discussion *iscussion "efore mid evaluation% *iscussion

)* +,-)* .id e/am .id ealuation 0aluation

11 30%10 Class discussion *iscussion after mid evaluation% *iscussion

160%11

#(4+$

7rdinar! differential e'uation

#7*+$, s!stem of simultaneous

7*+ and modeling using 7*+

unge(.utta method = &ultile unge(.utta method, )ater

tan, )ater "alance in a it, settling ond and serialinterconnected settling onds, "lasting, comrehensive

anal!sis of T22 and )ater ocet%

4ecture,discussion

13 16%118ui9

&odeling using 7*+

otes on The Boo of

2urface ater 8ualit! &odeling #7*+$ D -art I

4ecture,

discussion

13%11

#$

-roect

&odeling using 7*+ater -ocet

Grou

roect

-roect 5

&odeling using 7*+Comrehensive Anal!sis of T22

Grou

roect

1 1;%11-artial differential e'uation #-*+$,

modeling using -*+

*& solution of -*+: 1* and 6* stead! state, 1* and 6*

unstead! state, modeling natural resources evaluation

4ecture,

discussion

60%11

#$

-roect

&odeling using -*+&odeling coal mining and G flo)

Grou

roect

-roect @

&odeling using -*+Acid mine generation )ithin overurden stocile

Grou

roect

15 6%118ui9 @

&odeling using -*+

otes on The Boo of

2urface ater 8ualit! &odeling #-*+ ( 7*+$ D -art II

4ecture,

discussion

16@%11

#(4+$

8ui9 ?

&odeling using -*+

otes on The Boo of

2urface ater 8ualit! &odeling #-*+ ( 7*+$ D -art III

4ecture,

discussion

1@ 03%16 ra u = re final exam ro"lem Comrehensive T22 Anal!sis #7*+$ 4ecture,discussion

1?0%16

#(4+$ra u = re final exam ro"lem *istri"ution of T22 in 4ae and 2tream #7*+ D -*+$

4ecture,

discussion

), 1AS 2 Final 0/am Final ealuation 0aluation